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  Subjects -> COMPUTER SCIENCE (Total: 1964 journals)
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COMPUTER SCIENCE (1143 journals)                  1 2 3 4 5 6 | Last

Showing 1 - 200 of 872 Journals sorted alphabetically
3D Printing and Additive Manufacturing     Full-text available via subscription   (Followers: 11)
Abakós     Open Access   (Followers: 3)
Academy of Information and Management Sciences Journal     Full-text available via subscription   (Followers: 62)
ACM Computing Surveys     Hybrid Journal   (Followers: 21)
ACM Journal on Computing and Cultural Heritage     Hybrid Journal   (Followers: 6)
ACM Journal on Emerging Technologies in Computing Systems     Hybrid Journal   (Followers: 10)
ACM Transactions on Accessible Computing (TACCESS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Applied Perception (TAP)     Hybrid Journal   (Followers: 6)
ACM Transactions on Architecture and Code Optimization (TACO)     Hybrid Journal   (Followers: 7)
ACM Transactions on Autonomous and Adaptive Systems (TAAS)     Hybrid Journal   (Followers: 7)
ACM Transactions on Computation Theory (TOCT)     Hybrid Journal   (Followers: 10)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 2)
ACM Transactions on Computer Systems (TOCS)     Hybrid Journal   (Followers: 18)
ACM Transactions on Computer-Human Interaction     Hybrid Journal   (Followers: 12)
ACM Transactions on Computing Education (TOCE)     Hybrid Journal   (Followers: 2)
ACM Transactions on Design Automation of Electronic Systems (TODAES)     Hybrid Journal   (Followers: 1)
ACM Transactions on Economics and Computation     Hybrid Journal  
ACM Transactions on Embedded Computing Systems (TECS)     Hybrid Journal   (Followers: 4)
ACM Transactions on Information Systems (TOIS)     Hybrid Journal   (Followers: 19)
ACM Transactions on Intelligent Systems and Technology (TIST)     Hybrid Journal   (Followers: 9)
ACM Transactions on Interactive Intelligent Systems (TiiS)     Hybrid Journal   (Followers: 4)
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)     Hybrid Journal   (Followers: 7)
ACM Transactions on Reconfigurable Technology and Systems (TRETS)     Hybrid Journal   (Followers: 6)
ACM Transactions on Sensor Networks (TOSN)     Hybrid Journal   (Followers: 8)
ACM Transactions on Speech and Language Processing (TSLP)     Hybrid Journal   (Followers: 10)
ACM Transactions on Storage     Hybrid Journal  
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 19)
Acta Automatica Sinica     Full-text available via subscription   (Followers: 3)
Acta Universitatis Cibiniensis. Technical Series     Open Access  
Ad Hoc Networks     Hybrid Journal   (Followers: 11)
Adaptive Behavior     Hybrid Journal   (Followers: 10)
Advanced Engineering Materials     Hybrid Journal   (Followers: 22)
Advanced Science Letters     Full-text available via subscription   (Followers: 4)
Advances in Adaptive Data Analysis     Hybrid Journal   (Followers: 7)
Advances in Artificial Intelligence     Open Access   (Followers: 14)
Advances in Artificial Neural Systems     Open Access   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 4)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 14)
Advances in Computer Science : an International Journal     Open Access   (Followers: 13)
Advances in Computing     Open Access   (Followers: 2)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 42)
Advances in Engineering Software     Hybrid Journal   (Followers: 23)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Human Factors/Ergonomics     Full-text available via subscription   (Followers: 22)
Advances in Human-Computer Interaction     Open Access   (Followers: 18)
Advances in Materials Sciences     Open Access   (Followers: 15)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Parallel Computing     Full-text available via subscription   (Followers: 7)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Remote Sensing     Open Access   (Followers: 34)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Advances in Technology Innovation     Open Access  
AEU - International Journal of Electronics and Communications     Hybrid Journal   (Followers: 7)
African Journal of Information and Communication     Open Access   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 3)
Air, Soil & Water Research     Open Access   (Followers: 7)
AIS Transactions on Human-Computer Interaction     Open Access   (Followers: 6)
Algebras and Representation Theory     Hybrid Journal  
Algorithms     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 2)
American Journal of Computational Mathematics     Open Access   (Followers: 4)
American Journal of Information Systems     Open Access   (Followers: 5)
American Journal of Sensor Technology     Open Access   (Followers: 1)
Anais da Academia Brasileira de Ciências     Open Access   (Followers: 2)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 5)
Analysis in Theory and Applications     Hybrid Journal  
Animation Practice, Process & Production     Hybrid Journal   (Followers: 4)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 6)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 5)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of Software Engineering     Hybrid Journal   (Followers: 11)
Annual Reviews in Control     Hybrid Journal   (Followers: 6)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applied and Computational Harmonic Analysis     Full-text available via subscription   (Followers: 2)
Applied Artificial Intelligence: An International Journal     Hybrid Journal   (Followers: 12)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Computer Systems     Open Access   (Followers: 1)
Applied Informatics     Open Access  
Applied Mathematics and Computation     Hybrid Journal   (Followers: 32)
Applied Medical Informatics     Open Access   (Followers: 9)
Applied Numerical Analysis & Computational Mathematics     Hybrid Journal   (Followers: 5)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Soft Computing     Hybrid Journal   (Followers: 13)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 3)
Architectural Theory Review     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Artifact     Hybrid Journal   (Followers: 2)
Artificial Life     Hybrid Journal   (Followers: 5)
Asia Pacific Journal on Computational Engineering     Open Access  
Asia-Pacific Journal of Information Technology and Multimedia     Open Access   (Followers: 1)
Asian Journal of Control     Hybrid Journal  
Assembly Automation     Hybrid Journal   (Followers: 1)
at - Automatisierungstechnik     Hybrid Journal   (Followers: 1)
Australian Educational Computing     Open Access  
Automatic Control and Computer Sciences     Hybrid Journal   (Followers: 3)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 4)
Automatica     Hybrid Journal   (Followers: 8)
Automation in Construction     Hybrid Journal   (Followers: 6)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 7)
Basin Research     Hybrid Journal   (Followers: 3)
Behaviour & Information Technology     Hybrid Journal   (Followers: 53)
Bioinformatics     Hybrid Journal   (Followers: 199)
Biomedical Engineering     Hybrid Journal   (Followers: 15)
Biomedical Engineering and Computational Biology     Open Access   (Followers: 11)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (Followers: 16)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (Followers: 30)
Briefings in Bioinformatics     Hybrid Journal   (Followers: 43)
British Journal of Educational Technology     Hybrid Journal   (Followers: 108)
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 9)
CALCOLO     Hybrid Journal  
Calphad     Hybrid Journal  
Canadian Journal of Electrical and Computer Engineering     Full-text available via subscription   (Followers: 12)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
Cell Communication and Signaling     Open Access   (Followers: 1)
Central European Journal of Computer Science     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 2)
Chemometrics and Intelligent Laboratory Systems     Hybrid Journal   (Followers: 15)
ChemSusChem     Hybrid Journal   (Followers: 7)
China Communications     Full-text available via subscription   (Followers: 7)
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
CIN Computers Informatics Nursing     Full-text available via subscription   (Followers: 11)
Circuits and Systems     Open Access   (Followers: 13)
Clean Air Journal     Full-text available via subscription   (Followers: 2)
CLEI Electronic Journal     Open Access  
Clin-Alert     Hybrid Journal   (Followers: 1)
Cluster Computing     Hybrid Journal   (Followers: 1)
Cognitive Computation     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Communication Methods and Measures     Hybrid Journal   (Followers: 12)
Communication Theory     Hybrid Journal   (Followers: 17)
Communications Engineer     Hybrid Journal   (Followers: 1)
Communications in Algebra     Hybrid Journal   (Followers: 2)
Communications in Partial Differential Equations     Hybrid Journal   (Followers: 2)
Communications of the ACM     Full-text available via subscription   (Followers: 46)
Communications of the Association for Information Systems     Open Access   (Followers: 19)
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering     Hybrid Journal   (Followers: 3)
Complex Adaptive Systems Modeling     Open Access  
Complex Analysis and Operator Theory     Hybrid Journal   (Followers: 2)
Complexity     Hybrid Journal   (Followers: 6)
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Computación y Sistemas     Open Access  
Computation     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational and Structural Biotechnology Journal     Open Access   (Followers: 1)
Computational and Theoretical Chemistry     Hybrid Journal   (Followers: 9)
Computational Astrophysics and Cosmology     Open Access  
Computational Biology and Chemistry     Hybrid Journal   (Followers: 10)
Computational Chemistry     Open Access   (Followers: 2)
Computational Cognitive Science     Open Access  
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Condensed Matter     Open Access  
Computational Ecology and Software     Open Access   (Followers: 8)
Computational Economics     Hybrid Journal   (Followers: 9)
Computational Geosciences     Hybrid Journal   (Followers: 12)
Computational Linguistics     Open Access   (Followers: 22)
Computational Management Science     Hybrid Journal  
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Molecular Bioscience     Open Access   (Followers: 1)
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computational Particle Mechanics     Hybrid Journal   (Followers: 1)
Computational Research     Open Access   (Followers: 1)
Computational Science and Discovery     Full-text available via subscription   (Followers: 2)
Computational Science and Techniques     Open Access  
Computational Statistics     Hybrid Journal   (Followers: 14)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 27)
Computer     Full-text available via subscription   (Followers: 76)
Computer Aided Surgery     Hybrid Journal   (Followers: 3)
Computer Applications in Engineering Education     Hybrid Journal   (Followers: 6)
Computer Communications     Hybrid Journal   (Followers: 10)
Computer Engineering and Applications Journal     Open Access   (Followers: 5)
Computer Journal     Hybrid Journal   (Followers: 7)
Computer Methods in Applied Mechanics and Engineering     Hybrid Journal   (Followers: 20)
Computer Methods in Biomechanics and Biomedical Engineering     Hybrid Journal   (Followers: 10)
Computer Methods in the Geosciences     Full-text available via subscription   (Followers: 1)
Computer Music Journal     Hybrid Journal   (Followers: 13)
Computer Physics Communications     Hybrid Journal   (Followers: 6)
Computer Science - Research and Development     Hybrid Journal   (Followers: 7)
Computer Science and Engineering     Open Access   (Followers: 16)
Computer Science and Information Technology     Open Access   (Followers: 10)
Computer Science Education     Hybrid Journal   (Followers: 12)
Computer Science Journal     Open Access   (Followers: 21)
Computer Science Master Research     Open Access   (Followers: 9)
Computer Science Review     Hybrid Journal   (Followers: 10)
Computer Standards & Interfaces     Hybrid Journal   (Followers: 4)
Computer Supported Cooperative Work (CSCW)     Hybrid Journal   (Followers: 9)
Computer-aided Civil and Infrastructure Engineering     Hybrid Journal   (Followers: 9)
Computer-Aided Design and Applications     Hybrid Journal   (Followers: 2)

        1 2 3 4 5 6 | Last

Journal Cover Applied Numerical Mathematics
  [SJR: 1.254]   [H-I: 56]   [5 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0168-9274 - ISSN (Online) 0168-9274
   Published by Elsevier Homepage  [3038 journals]
  • High-order, stable, and efficient pseudospectral method using barycentric
           Gegenbauer quadratures
    • Authors: Kareem T. Elgindy
      Pages: 1 - 25
      Abstract: Publication date: March 2017
      Source:Applied Numerical Mathematics, Volume 113
      Author(s): Kareem T. Elgindy
      The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the well-conditioning of the numerical integration operators to produce well-conditioned systems of algebraic equations, which can be solved easily using standard algebraic system solvers. The core of the work lies in the derivation of novel and stable Gegenbauer quadratures based on the stable barycentric representation of Lagrange interpolating polynomials and the explicit barycentric weights for the Gegenbauer–Gauss (GG) points. A rigorous error and convergence analysis of the proposed quadratures is presented along with a detailed set of pseudocodes for the established computational algorithms. The proposed numerical scheme leads to a reduction in the computational cost and time complexity required for computing the numerical quadrature while sharing the same exponential order of accuracy achieved by Elgindy and Smith-Miles [14]. The bulk of the work includes three numerical test examples to assess the efficiency and accuracy of the numerical scheme. The present method provides a strong addition to the arsenal of numerical pseudospectral methods, and can be extended to solve a wide range of problems arising in numerous applications.

      PubDate: 2016-11-19T00:32:40Z
      DOI: 10.1016/j.apnum.2016.10.014
      Issue No: Vol. 113 (2016)
       
  • High-order, stable, and efficient pseudospectral method using barycentric
           Gegenbauer quadratures
    • Authors: Kareem T. Elgindy
      Pages: 1 - 25
      Abstract: Publication date: March 2017
      Source:Applied Numerical Mathematics, Volume 113
      Author(s): Kareem T. Elgindy
      The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the well-conditioning of the numerical integration operators to produce well-conditioned systems of algebraic equations, which can be solved easily using standard algebraic system solvers. The core of the work lies in the derivation of novel and stable Gegenbauer quadratures based on the stable barycentric representation of Lagrange interpolating polynomials and the explicit barycentric weights for the Gegenbauer–Gauss (GG) points. A rigorous error and convergence analysis of the proposed quadratures is presented along with a detailed set of pseudocodes for the established computational algorithms. The proposed numerical scheme leads to a reduction in the computational cost and time complexity required for computing the numerical quadrature while sharing the same exponential order of accuracy achieved by Elgindy and Smith-Miles [14]. The bulk of the work includes three numerical test examples to assess the efficiency and accuracy of the numerical scheme. The present method provides a strong addition to the arsenal of numerical pseudospectral methods, and can be extended to solve a wide range of problems arising in numerous applications.

      PubDate: 2016-11-19T00:32:40Z
      DOI: 10.1016/j.apnum.2016.10.014
      Issue No: Vol. 113 (2016)
       
  • Highly stable implicit–explicit Runge–Kutta methods
    • Authors: Giuseppe Izzo; Zdzislaw Jackiewicz
      Pages: 71 - 92
      Abstract: Publication date: March 2017
      Source:Applied Numerical Mathematics, Volume 113
      Author(s): Giuseppe Izzo, Zdzislaw Jackiewicz
      We investigate implicit–explicit (IMEX) Runge–Kutta (RK) methods for differential systems with non-stiff and stiff processes. The construction of such methods with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is A-stable, is described. We also describe the construction of IMEX RK methods, where the ‘explicit part’ of the schemes have strong stability properties. Examples of highly stable IMEX RK methods are provided up to the order p = 4 . Numerical examples are also given which illustrate good performance of these schemes.

      PubDate: 2016-12-01T00:40:27Z
      DOI: 10.1016/j.apnum.2016.10.018
      Issue No: Vol. 113 (2016)
       
  • Reconstruction of 3D scattered data via radial basis functions by
           efficient and robust techniques
    • Authors: Alberto Crivellaro; Simona Perotto; Stefano Zonca
      Pages: 93 - 108
      Abstract: Publication date: March 2017
      Source:Applied Numerical Mathematics, Volume 113
      Author(s): Alberto Crivellaro, Simona Perotto, Stefano Zonca
      We propose new algorithms to overcome two of the most constraining limitations of surface reconstruction methods in use. In particular, we focus on the large amount of data characterizing standard acquisitions by scanner and the noise intrinsically introduced by measurements. The first algorithm represents an adaptive multi-level interpolating approach, based on an implicit surface representation via radial basis functions. The second algorithm is based on a least-squares approximation to filter noisy data. The third approach combines the two algorithms to merge the correspondent improvements. An extensive numerical validation is performed to check the performances of the proposed techniques.

      PubDate: 2016-12-01T00:40:27Z
      DOI: 10.1016/j.apnum.2016.11.003
      Issue No: Vol. 113 (2016)
       
  • Non-monotone algorithm for minimization on arbitrary domains with
           applications to large-scale orthogonal Procrustes problem
    • Authors: J.B. Francisco; F.S. Viloche Bazán; M. Weber Mendonça
      Pages: 51 - 64
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): J.B. Francisco, F.S. Viloche Bazán, M. Weber Mendonça
      This paper concerns a non-monotone algorithm for minimizing differentiable functions on closed sets. A general numerical scheme is proposed which combines a regularization/trust-region framework with a non-monotone strategy. Global convergence to stationary points is proved under usual assumptions. Numerical experiments for a particular version of the general algorithm are reported. In addition, a promising numerical scheme for medium/large-scale orthogonal Procrustes problem is also proposed and numerically illustrated.

      PubDate: 2016-10-30T22:52:04Z
      DOI: 10.1016/j.apnum.2016.09.018
      Issue No: Vol. 112 (2016)
       
  • Well-balanced hybrid compact-WENO scheme for shallow water equations
    • Authors: Qiangqiang Zhu; Zhen Gao; Wai Sun Don; Xianqing Lv
      Pages: 65 - 78
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): Qiangqiang Zhu, Zhen Gao, Wai Sun Don, Xianqing Lv
      We investigate the performance of the high order well-balanced hybrid compact-weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for simulations of shallow water equations with source terms due to a non-flat bottom topography. The Hybrid scheme employs the nonlinear fifth order characteristic-wise WENO-Z finite difference scheme to capture high gradients and discontinuities in an essentially non-oscillatory manner, and the linear spectral-like sixth order compact finite difference scheme to resolve the fine scale structures in the smooth regions of the solution efficiently and accurately. The high order multi-resolution analysis is employed to identify the smoothness of the solution at each grid point. In this study, classical one- and two-dimensional simulations, including a long time two-dimensional dam-breaking problem with a non-flat bottom topography, are conducted to demonstrate the performance of the hybrid scheme in terms of the exact conservation property (C-property), good resolution and essentially non-oscillatory shock capturing of the smooth and discontinuous solutions respectively, and up to 2–3 times speedup factor over the well-balanced WENO-Z scheme.

      PubDate: 2016-11-05T23:42:19Z
      DOI: 10.1016/j.apnum.2016.10.001
      Issue No: Vol. 112 (2016)
       
  • A spectral iterative method for solving nonlinear singular Volterra
           integral equations of Abel type
    • Authors: A. Shoja; A.R. Vahidi; E. Babolian
      Pages: 79 - 90
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): A. Shoja, A.R. Vahidi, E. Babolian
      In this paper, a spectral iterative method is employed to obtain approximate solutions of singular nonlinear Volterra integral equations, called Abel type of Volterra integral equations. The Abel's type nonlinear Volterra integral equations are reduced to nonlinear fractional differential equations. This approach is based on a combination of two different methods, i.e. the iterative method proposed in [7] and the spectral method. The method reduces the fractional differential equations to systems of linear algebraic equations and then the resulting systems are solved by a numerical method. Finally, we prove that the spectral iterative method (SIM) is convergent. Numerical results comparing this iterative approach with alternative approaches offered in [4,8,24] are presented. Error estimation also corroborate numerically.

      PubDate: 2016-11-05T23:42:19Z
      DOI: 10.1016/j.apnum.2016.09.008
      Issue No: Vol. 112 (2016)
       
  • Fourth-order two-stage explicit exponential integrators for time-dependent
           PDEs
    • Authors: Vu Thai Luan
      Pages: 91 - 103
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): Vu Thai Luan
      Among the family of fourth-order time integration schemes, the two-stage Gauss–Legendre method, which is an implicit Runge–Kutta method based on collocation, is the only superconvergent. The computational cost of this implicit scheme for large systems, however, is very high since it requires solving a nonlinear system at every step. Surprisingly, in this work we show that one can construct and prove convergence results for exponential methods of order four which use two stages only. Specifically, we derive two new fourth-order two-stage exponential Rosenbrock schemes for solving large systems of differential equations. Moreover, since the newly schemes are not only superconvergent but also fully explicit, they turn out to be very competitive compared to the two-stage Gauss–Legendre method as well as other fourth-order time integration schemes. Numerical experiments are given to demonstrate the efficiency of the new integrators.

      PubDate: 2016-11-05T23:42:19Z
      DOI: 10.1016/j.apnum.2016.10.008
      Issue No: Vol. 112 (2016)
       
  • Adaptive multistep time discretization and linearization based on a
           posteriori error estimates for the Richards equation
    • Authors: V. Baron; Y. Coudière; P. Sochala
      Pages: 104 - 125
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): V. Baron, Y. Coudière, P. Sochala
      We derive some a posteriori error estimates for the Richards equation. This parabolic equation is nonlinear in space and in time, thus its resolution requires fixed-point iterations within each time step. We measure the approximation error with the dual norm of the residual. A computable upper bound of this error consists of several estimators involving adequate reconstructions based on the degrees of freedom of the scheme. The space and time reconstructions are specified for a two-step backward differentiation formula and a discrete duality finite volume scheme. Our strategy to decrease the computational cost relies on an aggregation of the estimators in three components: space discretization, time discretization, and linearization. We propose an algorithm to stop the fixed-point iterations after the linearization error becomes negligible, and to choose the time step in order to balance the time and space errors. We analyze the influence of the parameters of this algorithm on three test cases and quantify the gain obtained in comparison with a classical simulation.

      PubDate: 2016-11-05T23:42:19Z
      DOI: 10.1016/j.apnum.2016.10.005
      Issue No: Vol. 112 (2016)
       
  • Third order difference schemes (without using points outside of the
           domain) for one sided space tempered fractional partial differential
           equations
    • Authors: Yanyan Yu; Weihua Deng; Yujiang Wu; Jing Wu
      Pages: 126 - 145
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): Yanyan Yu, Weihua Deng, Yujiang Wu, Jing Wu
      Power-law probability density function (PDF) plays a key role in both subdiffusion and Lévy flights. However, sometimes because of the finiteness of the lifespan of the particles or the boundedness of the physical space, tempered power-law PDF seems to be a more physical choice and then the tempered fractional operators appear; in fact, the tempered fractional operators can also characterize the transitions among subdiffusion, normal diffusion, and Lévy flights. This paper focuses on the finite difference schemes for space tempered fractional diffusion equations, being much different from the ones for pure fractional derivatives. By using the generation function of the matrix and Weyl's theorem, the stability and convergence of the derived schemes are strictly proved. Some numerical simulations are performed to testify the effectiveness and numerical accuracy of the obtained schemes.

      PubDate: 2016-11-05T23:42:19Z
      DOI: 10.1016/j.apnum.2016.10.011
      Issue No: Vol. 112 (2016)
       
  • Topographical global initialization for finding all solutions of nonlinear
           systems with constraints
    • Authors: Nélio Henderson; Marroni de Sá Rêgo; Janaína Imbiriba
      Pages: 155 - 166
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): Nélio Henderson, Marroni de Sá Rêgo, Janaína Imbiriba
      We apply a recently revisited version of the topographical global initialization to solve nonlinear systems of equations with multiple roots subject to inequality constraints. This initialization technique is a simple and ingenious approach based on elementary concepts of graph theory. Here, the topographical initialization is used to generate good starting points to solve constrained global minimization problems, whose solutions are roots of associated nonlinear systems. To accomplish the task of local search, in the minimization step we use a well-established interior-point method. Our methodology was compared against other methods using benchmarks from the literature. Results indicated that the present approach is a powerful strategy for finding all roots of nonlinear systems.

      PubDate: 2016-11-05T23:42:19Z
      DOI: 10.1016/j.apnum.2016.10.007
      Issue No: Vol. 112 (2016)
       
  • Error analysis of first-order projection method for time-dependent
           magnetohydrodynamics equations
    • Authors: Rong An; Yuan Li
      Pages: 167 - 181
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): Rong An, Yuan Li
      This paper focuses on a linearized fully discrete projection scheme for time-dependent magnetohydrodynamics equations in three-dimensional bounded domain. It is shown that the proposed projection scheme allows for a discrete energy inequality and is unconditionally stable. In addition, we present a rigorous analysis for the rates of convergence.

      PubDate: 2016-11-13T00:16:13Z
      DOI: 10.1016/j.apnum.2016.10.010
      Issue No: Vol. 112 (2016)
       
  • Discontinuous Galerkin methods for a contact problem with Tresca friction
           arising in linear elasticity
    • Authors: Kamana Porwal
      Pages: 182 - 202
      Abstract: Publication date: February 2017
      Source:Applied Numerical Mathematics, Volume 112
      Author(s): Kamana Porwal
      In this article, we propose and analyze discontinuous Galerkin (DG) methods for a contact problem with Tresca friction for the linearized elastic material. We derive a residual based a posteriori error estimator for the proposed class of DG methods. The reliability and the efficiency of a posteriori error estimator is shown. We further investigate a priori error estimates under the minimal regularity assumption on the exact solution. An important property shared by a class of DG methods, allow us to carry out the analysis in a unified framework. Numerical experiments are reported to illustrate theoretical results.

      PubDate: 2016-11-13T00:16:13Z
      DOI: 10.1016/j.apnum.2016.10.012
      Issue No: Vol. 112 (2016)
       
  • A novel finite difference scheme for Burgers' equation on unbounded
           domains
    • Authors: Quan Zheng; Xin Zhao; Yufeng Liu
      Pages: 1 - 16
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): Quan Zheng, Xin Zhao, Yufeng Liu
      This paper studies a finite difference method for one-dimensional nonhomogeneous Burgers' equation on the infinite domain. Two exact nonlinear artificial boundary conditions are applied on two artificial boundaries to limit the original problem onto a bounded computational domain. A function transformation makes both Burgers' equation and artificial boundary conditions linear. Consequently, a novel finite difference scheme is developed by using the method of reduction of order for the obtained equation and artificial boundary conditions. The stability and the convergence with order 3/2 in time and 2 in space in an energy norm are proved for this method for Burgers' equation. Different examples illustrate the unconditional stability and the accuracy of the proposed method.

      PubDate: 2016-09-20T15:29:25Z
      DOI: 10.1016/j.apnum.2016.09.002
      Issue No: Vol. 111 (2016)
       
  • Discontinuous Galerkin methods with interior penalties on graded meshes
           for 2D singularly perturbed convection–diffusion problems
    • Authors: Yubo Yang; Peng Zhu
      Pages: 36 - 48
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): Yubo Yang, Peng Zhu
      In this paper, we introduce discontinuous Galerkin methods with interior penalties, both the NIPG and SIPG method for solving 2D singularly perturbed convection–diffusion problems. On the modified graded meshes with the standard Lagrange Q k -elements ( k = 1 , 2 ), we show optimal order error estimates in the ε-weighted energy norm uniformly, up to a logarithmic factor, in the singular perturbation parameter ε. We prove that the convergence rate in the ε-weighted energy norm is O ( log k + 1 ⁡ ( 1 ε ) N k ) , where the total number of the mesh points is O ( N 2 ) . For k ≥ 3 , our methods can be extended directly, provided the higher order regularities of the solution u are derived. Finally, numerical experiments support our theoretical results.

      PubDate: 2016-09-24T15:42:25Z
      DOI: 10.1016/j.apnum.2016.09.004
      Issue No: Vol. 111 (2016)
       
  • High-order numerical schemes based on difference potentials for 2D
           elliptic problems with material interfaces
    • Authors: Jason Albright; Yekaterina Epshteyn; Michael Medvinsky; Qing Xia
      Pages: 64 - 91
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): Jason Albright, Yekaterina Epshteyn, Michael Medvinsky, Qing Xia
      Numerical approximations and computational modeling of problems from Biology and Materials Science often deal with partial differential equations with varying coefficients and domains with irregular geometry. The challenge here is to design an efficient and accurate numerical method that can resolve properties of solutions in different domains/subdomains, while handling the arbitrary geometries of the domains. In this work, we consider 2D elliptic models with material interfaces and develop efficient high-order accurate methods based on Difference Potentials for such problems.

      PubDate: 2016-09-24T15:42:25Z
      DOI: 10.1016/j.apnum.2016.08.017
      Issue No: Vol. 111 (2016)
       
  • Approximate Gauss–Newton methods for solving underdetermined
           nonlinear least squares problems
    • Authors: Ji-Feng Bao; Chong Li; Wei-Ping Shen; Jen-Chih Yao; Sy-Ming Guu
      Pages: 92 - 110
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): Ji-Feng Bao, Chong Li, Wei-Ping Shen, Jen-Chih Yao, Sy-Ming Guu
      We propose several approximate Gauss–Newton methods, i.e., the truncated, perturbed, and truncated-perturbed GN methods, for solving underdetermined nonlinear least squares problems. Under the assumption that the Fréchet derivatives are Lipschitz continuous and of full row rank, Kantorovich-type convergence criteria of the truncated GN method are established and local convergence theorems are presented with the radii of convergence balls obtained. As consequences of the convergence results for the truncated GN method, convergence theorems of the perturbed and truncated-perturbed GN methods are also presented. Finally, numerical experiments are presented where the comparisons with the standard inexact Gauss–Newton method and the inexact trust-region method for bound-constrained least squares problems [23] are made.

      PubDate: 2016-09-24T15:42:25Z
      DOI: 10.1016/j.apnum.2016.08.007
      Issue No: Vol. 111 (2016)
       
  • An improved semi-Lagrangian time splitting spectral method for the
           semi-classical Schrödinger equation with vector potentials using NUFFT
    • Authors: Zheng Ma; Yong Zhang; Zhennan Zhou
      Pages: 144 - 159
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): Zheng Ma, Yong Zhang, Zhennan Zhou
      In this paper, we propose a new time splitting Fourier spectral method for the semi-classical Schrödinger equation with vector potentials. Compared with the results in [21], our method achieves spectral accuracy in space by interpolating the Fourier series via the NonUniform Fast Fourier Transform (NUFFT) algorithm in the convection step. The NUFFT algorithm helps maintain high spatial accuracy of Fourier method, and at the same time improve the efficiency from O ( N 2 ) (of direct computation) to O ( N log ⁡ N ) operations, where N is the total number of grid points. The kinetic step and potential step are solved by analytical solution with pseudo-spectral approximation, and, therefore, we obtain spectral accuracy in space for the whole method. We prove that the method is unconditionally stable, and we show improved error estimates for both the wave function and physical observables, which agree with the results in [3] for vanishing potential cases and are superior to those in [21]. Extensive one and two dimensional numerical studies are presented to verify the properties of the proposed method, and simulations of 3D problems are demonstrated to show its potential for future practical applications.

      PubDate: 2016-09-24T15:42:25Z
      DOI: 10.1016/j.apnum.2016.08.015
      Issue No: Vol. 111 (2016)
       
  • Identification of the zeroth-order coefficient in a time fractional
           diffusion equation
    • Authors: Liangliang Sun; Ting Wei
      Pages: 160 - 180
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): Liangliang Sun, Ting Wei
      This paper is devoted to identify the zeroth-order coefficient in a time-fractional diffusion equation from two boundary measurement data in one-dimensional case. The existence and uniqueness of two kinds of weak solutions for the direct problem with Neumann boundary condition are proved. We provide the uniqueness for recovering the zeroth-order coefficient and fractional order simultaneously by the Laplace transformation and Gel'fand–Levitan theory. The identification of the zeroth-order coefficient is formulated into a variational problem by the Tikhonov regularization. The existence, stability and convergence of the solution for the variational problem are provided. We deduce an adjoint problem and then use a conjugate gradient method to solve the variational problem. Two numerical examples are provided to show the effectiveness of the proposed method.

      PubDate: 2016-09-28T16:12:38Z
      DOI: 10.1016/j.apnum.2016.09.005
      Issue No: Vol. 111 (2016)
       
  • An adaptive meshless local Petrov–Galerkin method based on a posteriori
           error estimation for the boundary layer problems
    • Authors: Maryam Kamranian; Mehdi Dehghan; Mehdi Tatari
      Pages: 181 - 196
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): Maryam Kamranian, Mehdi Dehghan, Mehdi Tatari
      A new adaptive moving least squares (MLS) method with variable radius of influence is presented to improve the accuracy of Meshless Local Petrov–Galerkin (MLPG) methods and to minimize the computational cost for the numerical solution of singularly perturbed boundary value problems. An error indicator based on a posteriori error estimation, accurately captures the regions of the domain with insufficient resolution and adaptively determines the new nodes location. The effectiveness of the new method is demonstrated on some singularly perturbed problems involving boundary layers.

      PubDate: 2016-10-19T03:15:34Z
      DOI: 10.1016/j.apnum.2016.09.007
      Issue No: Vol. 111 (2016)
       
  • An improved collocation method for multi-dimensional space–time
           variable-order fractional Schrödinger equations
    • Authors: A.H. Bhrawy; M.A. Zaky
      Pages: 197 - 218
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): A.H. Bhrawy, M.A. Zaky
      Current discretizations of variable-order fractional (V-OF) differential equations lead to numerical solutions of low order of accuracy. This paper explores a high order numerical scheme for multi-dimensional V-OF Schrödinger equations. We derive new operational matrices for the V-OF derivatives of Caputo and Riemann–Liouville type of the shifted Jacobi polynomials (SJPs). These allow us to establish an efficient approximate formula for the Riesz fractional derivative. An operational approach of the Jacobi collocation approach for the approximate solution of the V-OF nonlinear Schrödinger equations. The main characteristic behind this approach is to investigate a space–time spectral approximation for spatial and temporal discretizations. The proposed spectral scheme, both in temporal and spatial discretizations, is successfully developed to handle the two-dimensional V-OF Schrödinger equation. Numerical results indicating the spectral accuracy and effectiveness of this algorithm are presented.

      PubDate: 2016-10-05T16:57:23Z
      DOI: 10.1016/j.apnum.2016.09.009
      Issue No: Vol. 111 (2016)
       
  • Convergence and error estimates of viscosity-splitting finite-element
           schemes for the primitive equations
    • Authors: F. Guillén-González; M.V. Redondo-Neble
      Pages: 219 - 245
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): F. Guillén-González, M.V. Redondo-Neble
      This paper is devoted to the numerical analysis of a first order fractional-step time-scheme (via decomposition of the viscosity) and “inf-sup” stable finite-element spatial approximations applied to the Primitive Equations of the Ocean. The aim of the paper is twofold. First, we prove that the scheme is unconditionally stable and convergent towards weak solutions of the Primitive Equations. Second, optimal error estimates for velocity and pressure are provided of order O ( k + h l ) for l = 1 or l = 2 considering either first or second order finite-element approximations (k and h being the time step and the mesh size, respectively). In both cases, these error estimates are obtained under the same constraint k ≤ C h 2 .

      PubDate: 2016-10-05T16:57:23Z
      DOI: 10.1016/j.apnum.2016.09.011
      Issue No: Vol. 111 (2016)
       
  • Multidomain Legendre–Galerkin Chebyshev-collocation method for
           one-dimensional evolution equations with discontinuity
    • Authors: Heping Ma; Yonghui Qin; Qiuli Ou
      Pages: 246 - 259
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): Heping Ma, Yonghui Qin, Qiuli Ou
      The multidomain Legendre–Galerkin Chebyshev-collocation method is considered to solve one-dimensional linear evolution equations with two nonhomogeneous jump conditions. The scheme treats the first jump condition essentially and the second one naturally. We adopt appropriate base functions to deal with interfaces. The proposed method can be implemented in parallel. Error analysis shows that the approach has an optimal convergence rate. The proposed method is also applied to computing the one-dimensional Maxwell equation and the one-dimensional two phase Stefan problem, respectively. Numerical examples are given to confirm the theoretical analysis.

      PubDate: 2016-10-05T16:57:23Z
      DOI: 10.1016/j.apnum.2016.09.010
      Issue No: Vol. 111 (2016)
       
  • Degenerate tetrahedra removal
    • Authors: Franco Dassi; Luca Formaggia; Stefano Zonca
      Pages: 1 - 13
      Abstract: Publication date: December 2016
      Source:Applied Numerical Mathematics, Volume 110
      Author(s): Franco Dassi, Luca Formaggia, Stefano Zonca
      Standard 3D mesh generation algorithms may produce a low quality tetrahedral mesh, i.e., a mesh where the tetrahedra have very small dihedral angles. In this paper, we propose a series of operations to recover these badly-shaped tetrahedra. In particular, we will focus on the shape of these undesired mesh elements by proposing a novel method to distinguish and classify them. For each of these configurations, we apply a suitable sequence of operations to get a higher mesh quality. Finally, we employ a random algorithm to avoid locks and loops in the procedure. The reliability of the proposed mesh optimization algorithm is numerically proved with several examples.

      PubDate: 2016-08-18T06:09:52Z
      DOI: 10.1016/j.apnum.2016.07.013
      Issue No: Vol. 110 (2016)
       
  • The basins of attraction of Murakami's fifth order family of methods
    • Authors: Changbum Chun; Beny Neta
      Pages: 14 - 25
      Abstract: Publication date: Available online 3 August 2016
      Source:Applied Numerical Mathematics
      Author(s): Changbum Chun, Beny Neta
      In this paper we analyze Murakami's family of fifth order methods for the solution of nonlinear equations. We show how to find the best performer by using a measure of closeness of the extraneous fixed points to the imaginary axis. We demonstrate the performance of these members as compared to the two members originally suggested by Murakami. We found several members for which the extraneous fixed points are on the imaginary axis, only one of these has 6 such points (compared to 8 for the other members). We show that this member is the best performer.

      PubDate: 2016-08-18T06:09:52Z
      DOI: 10.1016/j.apnum.2016.07.012
      Issue No: Vol. 110 (2016)
       
  • A fixed grid, shifted stencil scheme for inviscid fluid-particle
           interaction
    • Authors: John D. Towers
      Pages: 26 - 40
      Abstract: Publication date: Available online 12 August 2016
      Source:Applied Numerical Mathematics
      Author(s): John D. Towers
      This paper presents a finite volume scheme for a scalar one-dimensional fluid-particle interaction model. When devising a finite volume scheme for this model, one difficulty that arises is how to deal with the moving source term in the PDE while maintaining a fixed grid. The fixed grid requirement comes from the ultimate goal of accommodating two or more particles. The finite volume scheme that we propose addresses the moving source term in a novel way. We use a modified computational stencil, with the lower part of the stencil shifted during those time steps when the particle crosses a mesh point. We then employ an altered convective flux to compensate the stencil shifts. The resulting scheme uses a fixed grid, preserves total momentum, and enforces several stability properties in the single-particle case. The single-particle scheme is easily extended to multiple particles by a splitting method.

      PubDate: 2016-08-18T06:09:52Z
      DOI: 10.1016/j.apnum.2016.08.002
      Issue No: Vol. 110 (2016)
       
  • Spectral semi-implicit and space–time discontinuous Galerkin methods for
           
    • Authors: Francesco Fambri; Michael Dumbser
      Pages: 41 - 74
      Abstract: Publication date: Available online 3 August 2016
      Source:Applied Numerical Mathematics
      Author(s): Francesco Fambri, Michael Dumbser
      In this paper two new families of arbitrary high order accurate spectral discontinuous Galerkin (DG) finite element methods are derived on staggered Cartesian grids for the solution of the incompressible Navier–Stokes (NS) equations in two and three space dimensions. The discrete solutions of pressure and velocity are expressed in the form of piecewise polynomials along different meshes. While the pressure is defined on the control volumes of the main grid, the velocity components are defined on edge-based dual control volumes, leading to a spatially staggered mesh. Thanks to the use of a nodal basis on a tensor-product domain, all discrete operators can be written efficiently as a combination of simple one-dimensional operators in a dimension-by-dimension fashion. In the first family, high order of accuracy is achieved only in space, while a simple semi-implicit time discretization is derived by introducing an implicitness factor θ ∈ [ 0.5 , 1 ] for the pressure gradient in the momentum equation. The real advantages of the staggering arise after substituting the discrete momentum equation into the weak form of the continuity equation. In fact, the resulting linear system for the pressure is symmetric and positive definite and either block penta-diagonal (in 2D) or block hepta-diagonal (in 3D). As a consequence, the pressure system can be solved very efficiently by means of a classical matrix-free conjugate gradient method. From our numerical experiments we find that the pressure system appears to be reasonably well-conditioned, since in all test cases shown in this paper the use of a preconditioner was not necessary. This is a rather unique feature among existing implicit DG schemes for the Navier–Stokes equations. In order to avoid a stability restriction due to the viscous terms, the latter are discretized implicitly using again a staggered mesh approach, where the viscous stress tensor is also defined on the dual mesh. The second family of staggered DG schemes proposed in this paper achieves high order of accuracy also in time by expressing the numerical solution in terms of piecewise space–time polynomials. In order to circumvent the low order of accuracy of the adopted fractional stepping, a simple iterative Picard procedure is introduced, which leads to a space–time pressure-correction algorithm. In this manner, the symmetry and positive definiteness of the pressure system are not compromised. The resulting algorithm is stable, computationally very efficient, and at the same time arbitrary high order accurate in both space and time. These features are typically not easy to obtain all at the same time for a numerical method applied to the incompressible Navier–Stokes equations. The new numerical method has been thoroughly validated for approximation polynomials of degree up to N = 11 , using a large set of non-trivial test problems in two and three space dimensions, for which either analytical, numerical or experimental reference solutions exist.

      PubDate: 2016-08-18T06:09:52Z
      DOI: 10.1016/j.apnum.2016.07.014
      Issue No: Vol. 110 (2016)
       
  • A nonlinear time-dependent radiation condition for simulations of internal
           gravity waves in geophysical fluid flows
    • Authors: V. Nijimbere; L.J. Campbell
      Pages: 75 - 92
      Abstract: Publication date: Available online 12 August 2016
      Source:Applied Numerical Mathematics
      Author(s): V. Nijimbere, L.J. Campbell
      This paper examines the development of a time-dependent nonreflecting boundary condition (or radiation condition) for use in simulations of the propagation of internal gravity waves in a two-dimensional geophysical fluid flow configuration. First, a linear radiation condition, originally derived by Campbell and Maslowe, is implemented in some linear test cases. It involves the computation of a Laplace convolution integral which is nonlocal in time and thus requires values of the dependent variable at all previous time levels. An approximation for the integral is implemented here to reduce the expense of the computation and the results obtained are shown to be more accurate than those obtained using steady boundary conditions. For larger amplitude waves, nonlinear equations are required and the application of the linear radiation condition gives rise to instabilities. A new nonlinear time-dependent nonreflecting boundary condition is introduced which takes into account wave mean flow interactions in the vicinity of the outflow boundary by including a component corresponding to the vertical divergence of the horizontal momentum flux. This prevents the development of numerical instabilities and gives more accurate results in a nonlinear test problem than the results obtained using the linear radiation condition.

      PubDate: 2016-08-18T06:09:52Z
      DOI: 10.1016/j.apnum.2016.08.001
      Issue No: Vol. 110 (2016)
       
  • Analysis of a family of continuous–discontinuous Galerkin FEM for
           convection–diffusion problems
    • Authors: Sebastian Franz
      Pages: 93 - 109
      Abstract: Publication date: Available online 20 August 2016
      Source:Applied Numerical Mathematics
      Author(s): Sebastian Franz
      It is well known that continuous Galerkin methods lack stability for singularly perturbed convection-diffusion problems. One approach to overcome this behaviour is to use discontinuous Galerkin methods instead. Unfortunately, this increases the number of degrees of freedom and thus the computational costs. We analyse discontinuous Galerkin methods of anisotropic polynomial order and discrete discontinuous spaces. By enforcing continuity in the vertices of a mesh, the number of unknowns can be reduced while the convergence order in the dG-norm is still sustained. Numerical experiments for several polynomial elements and finite element spaces support our theoretical results.

      PubDate: 2016-08-23T07:58:42Z
      DOI: 10.1016/j.apnum.2016.08.004
      Issue No: Vol. 110 (2016)
       
  • A reconstructed central discontinuous Galerkin-finite element method for
           the fully nonlinear weakly dispersive Green–Naghdi model
    • Authors: Haiyun Dong; Maojun Li
      Pages: 110 - 127
      Abstract: Publication date: December 2016
      Source:Applied Numerical Mathematics, Volume 110
      Author(s): Haiyun Dong, Maojun Li
      In this paper, we present a class of high order reconstructed central discontinuous Galerkin-finite element methods for the fully nonlinear weakly dispersive Green–Naghdi model, which describes a large spectrum of shallow water waves. In the proposed methods, we first reformulate the Green–Naghdi model into conservation laws coupled with an elliptic equation, and then discretize the conservation laws with reconstructed central discontinuous Galerkin methods and the elliptic equation with continuous FE methods. The reconstructed central discontinuous Galerkin methods can be viewed as a class of fast central discontinuous Galerkin methods, in which we replace the standard formula for the numerical solution defined on the dual mesh in the central discontinuous Galerkin method with a projection equation in the L 2 sense. The proposed methods reduce the computational cost of the traditional methods by nearly half but still maintain the formal high order accuracy. We study the L 2 stability and an L 2 a priori error estimate for smooth solutions of the reconstructed central discontinuous Galerkin method for linear hyperbolic equation. Numerical tests are presented to illustrate the accuracy and computational efficiency of the proposed method.

      PubDate: 2016-09-09T16:28:07Z
      DOI: 10.1016/j.apnum.2016.08.008
      Issue No: Vol. 110 (2016)
       
  • Two-point boundary value problems associated to functional differential
           equations of even order solved by iterated splines
    • Authors: Alexandru Mihai Bica; Mircea Curila; Sorin Curila
      Pages: 128 - 147
      Abstract: Publication date: December 2016
      Source:Applied Numerical Mathematics, Volume 110
      Author(s): Alexandru Mihai Bica, Mircea Curila, Sorin Curila
      A new iterative numerical method to solve two-point boundary value problems associated to functional differential equations of even order is proposed. The method uses a cubic spline interpolation procedure activated at each iterative step. The convergence of the method is proved and it is tested on some numerical experiments. The notion of numerical stability with respect to the choice of the first iteration is introduced proving that the proposed method is numerically stable in this sense.

      PubDate: 2016-09-09T16:28:07Z
      DOI: 10.1016/j.apnum.2016.08.003
      Issue No: Vol. 110 (2016)
       
  • The Fibonacci family of iterative processes for solving nonlinear
           equations
    • Authors: Tamara Kogan; Luba Sapir; Amir Sapir; Ariel Sapir
      Pages: 148 - 158
      Abstract: Publication date: Available online 30 August 2016
      Source:Applied Numerical Mathematics
      Author(s): Tamara Kogan, Luba Sapir, Amir Sapir, Ariel Sapir
      This paper presents a class of stationary iterative processes with convergence order equal to the growth rate of generalized Fibonacci sequences. We prove that the informational and computational efficiency of the processes of our class tend to 2 from below. The paper illustrates a connection of the methods of the class with the nonstationary iterative method suggested by our previous paper, whose efficiency index equals to 2. We prove that the efficiency of the nonstationary iterative method, measured by Ostrowski-Traub criteria, is maximal among all iterative processes of order 2.

      PubDate: 2016-08-31T15:40:36Z
      DOI: 10.1016/j.apnum.2016.08.012
      Issue No: Vol. 110 (2016)
       
  • A radial basis function based implicit–explicit method for option
           pricing under jump-diffusion models
    • Authors: Mohan K. Kadalbajoo; Alpesh Kumar; Lok Pati Tripathi
      Pages: 159 - 173
      Abstract: Publication date: December 2016
      Source:Applied Numerical Mathematics, Volume 110
      Author(s): Mohan K. Kadalbajoo, Alpesh Kumar, Lok Pati Tripathi
      In this article, we present a radial basis function based implicit explicit numerical method to solve the partial integro-differential equation which describes the nature of the option price under jump diffusion model. The governing equation is time semi discrtized by using the implicit–explicit backward difference method of order two (IMEX-BDF2) followed by radial basis function based finite difference (RBF-FD) method. The numerical scheme derived for European option is extended for American option by using operator splitting method. Numerical results for put and call option under Merton and Kou models are given to illustrate the efficiency and accuracy of the present method. The stability of time semi discretized scheme is also proved.

      PubDate: 2016-09-20T15:29:25Z
      DOI: 10.1016/j.apnum.2016.08.006
      Issue No: Vol. 110 (2016)
       
  • The inexact-Newton via GMRES subspace method without line search technique
           for solving symmetric nonlinear equations
    • Authors: Jueyu Wang; Detong Zhu
      Pages: 174 - 189
      Abstract: Publication date: Available online 30 August 2016
      Source:Applied Numerical Mathematics
      Author(s): Jueyu Wang, Detong Zhu
      In this paper, we propose an inexact-Newton via GMRES (generalized minimal residual) subspace method without line search technique for solving symmetric nonlinear equations. The iterative direction is obtained by solving the Newton equation of the system of nonlinear equations with the GMRES algorithm. The global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed algorithm.

      PubDate: 2016-08-31T15:40:36Z
      DOI: 10.1016/j.apnum.2016.08.013
      Issue No: Vol. 110 (2016)
       
  • Nanostructures imaging via numerical solution of a 3-D inverse scattering
           problem without the phase information
    • Authors: Michael V. Klibanov; Loc H. Nguyen; Kejia Pan
      Pages: 190 - 203
      Abstract: Publication date: December 2016
      Source:Applied Numerical Mathematics, Volume 110
      Author(s): Michael V. Klibanov, Loc H. Nguyen, Kejia Pan
      Inverse scattering problems without the phase information arise in imaging of nanostructures, whose sizes are hundreds of nanometers, as well as in imaging of biological cells. The governing equation is the 3-D generalized Helmholtz equation with the unknown coefficient, which represents the spatially distributed dielectric constant. It is assumed in the classical inverse scattering problem that both the modulus and the phase of the complex valued scattered wave field are measured outside of a scatterer. Unlike this, it is assumed here that only the modulus of the complex valued scattered wave field is measured on a certain interval of frequencies. The phase is not measured. In this paper a substantially modified reconstruction procedure of [25] is developed and numerically implemented. Ranges of parameters, which are realistic for imaging of nanostructures, are used in numerical examples. Note that numerical studies were not carried out in [25].

      PubDate: 2016-09-20T15:29:25Z
      DOI: 10.1016/j.apnum.2016.08.014
      Issue No: Vol. 110 (2016)
       
  • Spline collocation for fractional weakly singular integro-differential
           equations
    • Authors: Arvet Pedas; Enn Tamme; Mikk Vikerpuur
      Pages: 204 - 214
      Abstract: Publication date: December 2016
      Source:Applied Numerical Mathematics, Volume 110
      Author(s): Arvet Pedas, Enn Tamme, Mikk Vikerpuur
      We consider a class of boundary value problems for linear fractional weakly singular integro-differential equations which involve Caputo-type derivatives. Using an integral equation reformulation of the boundary value problem, we first study the regularity of the exact solution. Based on the obtained regularity properties and spline collocation techniques, the numerical solution of the boundary value problem by suitable non-polynomial approximations is discussed. Optimal global convergence estimates are derived and a super-convergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented.

      PubDate: 2016-09-24T15:42:25Z
      DOI: 10.1016/j.apnum.2016.07.011
      Issue No: Vol. 110 (2016)
       
  • On the decay rate of Chebyshev coefficients
    • Authors: Hassan Majidian
      Abstract: Publication date: Available online 16 November 2016
      Source:Applied Numerical Mathematics
      Author(s): Hassan Majidian
      It is well known that the coefficients of the Chebyshev expansion of a function f ∈ C [ − 1 , 1 ] decay at a rate depending on the smoothness of f. New decay rates for the Chebyshev coefficients as well as their partial sums are obtained which are sharper than those proposed so far.

      PubDate: 2016-11-19T00:32:40Z
      DOI: 10.1016/j.apnum.2016.11.004
       
  • Multi-step Runge–Kutta–Nyström methods for special second-order
           initial value problems
    • Authors: Jiyong Li; Xianfen Wang
      Abstract: Publication date: Available online 17 November 2016
      Source:Applied Numerical Mathematics
      Author(s): Jiyong Li, Xianfen Wang
      In this paper, multi-step Runge–Kutta–Nyström methods for the numerical integration of special second-order initial value problems are proposed and studied. These methods include classical Runge–Kutta–Nyström methods as special cases. General order conditions are derived by using the theory of B-series based on the set of special Nyström-trees, and two explicit methods with order five and six, respectively, are constructed. Numerical results show that our new methods are more efficient in comparison with classical Runge–Kutta–Nyström methods and other well-known high quality methods proposed in the scientific literature.

      PubDate: 2016-11-19T00:32:40Z
      DOI: 10.1016/j.apnum.2016.11.002
       
  • Approximating the leading singular triplets of a large matrix function
    • Authors: Sarah W. Gaaf; Valeria Simoncini
      Abstract: Publication date: Available online 5 November 2016
      Source:Applied Numerical Mathematics
      Author(s): Sarah W. Gaaf, Valeria Simoncini
      Given a large square matrix A and a sufficiently regular function f so that f ( A ) is well defined, we are interested in the approximation of the leading singular values and corresponding left and right singular vectors of f ( A ) , and in particular in the approximation of ‖ f ( A ) ‖ , where ‖ ⋅ ‖ is the matrix norm induced by the Euclidean vector norm. Since neither f ( A ) nor f ( A ) v can be computed exactly, we introduce a new inexact Golub–Kahan–Lanczos bidiagonalization procedure, where the inexactness is related to the inaccuracy of the operations f ( A ) v , f ( A ) ⁎ v . Particular outer and inner stopping criteria are devised so as to cope with the lack of a true residual. Numerical experiments with the new algorithm on typical application problems are reported.

      PubDate: 2016-11-05T23:42:19Z
      DOI: 10.1016/j.apnum.2016.10.015
       
  • Convergence of Newton, Halley and Chebyshev iterative methods as methods
           for simultaneous determination of multiple polynomial zeros
    • Authors: Veselina K. Kyncheva; Viktor V. Yotov; Stoil I. Ivanov
      Abstract: Publication date: Available online 29 October 2016
      Source:Applied Numerical Mathematics
      Author(s): Veselina K. Kyncheva, Viktor V. Yotov, Stoil I. Ivanov
      In this paper, we provide a local convergence analysis of Newton, Halley and Chebyshev iterative methods considered as methods for simultaneous determination of all multiple zeros of a polynomial f over an arbitrary normed field K . Convergence theorems with a priori and a posteriori error estimates for each of the proposed methods are established. The obtained results for Newton and Chebyshev methods are new even in the case of simple zeros. Three numerical examples are given to compare the convergence properties of the considered methods and to confirm the theoretical results.

      PubDate: 2016-10-30T22:52:04Z
      DOI: 10.1016/j.apnum.2016.10.013
       
  • Totally positive refinable functions with general dilation M
    • Authors: Laura Gori; Francesca Pitolli
      Abstract: Publication date: Available online 11 October 2016
      Source:Applied Numerical Mathematics
      Author(s): Laura Gori, Francesca Pitolli
      We construct a new class of approximating functions that are M-refinable and provide shape preserving approximations. The refinable functions in the class are smooth, compactly supported, centrally symmetric and totally positive. Moreover, their refinable masks are associated with convergent subdivision schemes. The presence of one or more shape parameters gives a great flexibility in the applications. Some examples for dilation M = 4 and M = 5 are also given.

      PubDate: 2016-10-12T02:54:02Z
      DOI: 10.1016/j.apnum.2016.10.004
       
  • Order-preserving strong schemes for SDEs with locally Lipschitz
           coefficients
    • Authors: Zhongqiang Zhang; Heping Ma
      Abstract: Publication date: Available online 8 October 2016
      Source:Applied Numerical Mathematics
      Author(s): Zhongqiang Zhang, Heping Ma
      We introduce a class of explicit balanced schemes for stochastic differential equations with coefficients of superlinearly growth satisfying a global monotone condition. The first scheme is a balanced Euler scheme and is of order half in the mean-square sense whereas it is of order one under additive noise. The second scheme is a balanced Milstein scheme, which is of order one in the mean-square sense. Some numerical results are presented.

      PubDate: 2016-10-12T02:54:02Z
      DOI: 10.1016/j.apnum.2016.09.013
       
  • A RBF-WENO finite volume method for hyperbolic conservation laws with the
           monotone polynomial interpolation method
    • Authors: Jingyang Guo; Jae-Hun Jung
      Abstract: Publication date: Available online 11 October 2016
      Source:Applied Numerical Mathematics
      Author(s): Jingyang Guo, Jae-Hun Jung
      Essentially non-oscillatory (ENO) and weighted ENO (WENO) methods are efficient high order numerical methods for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations. The original ENO and WENO methods are based on the polynomial interpolation and the overall convergence rate is uniquely determined by the total number of interpolation points involved for the approximation. In this paper, we propose non-polynomial ENO and WENO finite volume methods in order to enhance the local accuracy and convergence. The infinitely smooth radial basis functions (RBFs) are adopted as a non-polynomial interpolation basis. Particularly we use the multi-quadratic and Gaussian RBFs. The non-polynomial interpolation such as the RBF interpolation offers the flexibility to control the local error by optimizing the free parameter. Then we show that the non-polynomial interpolation can be represented as a perturbation of the polynomial interpolation. To guarantee the essentially non-oscillatory property, the monotone polynomial interpolation method is introduced as a switching method to the polynomial reconstruction adaptively near the non-smooth area. The numerical results show that the developed non-polynomial ENO and WENO methods with the monotone polynomial interpolation method enhance the local accuracy and give sharper solution profile.

      PubDate: 2016-10-12T02:54:02Z
      DOI: 10.1016/j.apnum.2016.10.003
       
  • Accurate cubature and extended Kalman filtering methods for estimating
           continuous-time nonlinear stochastic systems with discrete measurements
    • Authors: G.Yu. Kulikov; M.V. Kulikova
      Abstract: Publication date: Available online 3 October 2016
      Source:Applied Numerical Mathematics
      Author(s): G.Yu. Kulikov, M.V. Kulikova
      This paper further advances the idea of accurate Gaussian filtering towards efficient cubature Kalman filters for estimating continuous-time nonlinear stochastic systems with discrete measurements. It implies that the moment differential equations describing evolution of the predicted mean and covariance of the propagated Gaussian density in time are solved accurately, i.e. with negligible error. The latter allows the total error of the cubature Kalman filtering to be reduced significantly and results in a new accurate continuous-discrete cubature Kalman filtering method. At the same time, we revise the earlier developed version of the accurate continuous-discrete extended Kalman filter by amending the involved iteration and relaxing the utilized global error control mechanism. In addition, we build a mixed-type method, which unifies the best features of the accurate continuous-discrete extended and cubature Kalman filters. More precisely, the time updates are done in this state estimator as those in the first filter whereas the measurement updates are conducted with use of the third-degree spherical-radial cubature rule applied for approximating the arisen Gaussian-weighted integrals. All these are examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, and compared to the state-of-the-art cubature Kalman filters.

      PubDate: 2016-10-05T16:57:23Z
       
  • Convergent interpolatory quadrature schemes
    • Authors: Fidalgo
      Abstract: Publication date: January 2017
      Source:Applied Numerical Mathematics, Volume 111
      Author(s): U. Fidalgo
      We use a connection between interpolatory quadrature formulas and Fourier series to find a wide class of convergent schemes of interpolatory quadrature rules. In the process we use techniques coming from Riemann–Hilbert problems for varying measures and convex analysis.

      PubDate: 2016-09-24T15:42:25Z
       
  • Fourier Collocation Algorithm for identification of a spacewise dependent
           source in wave equation from Neumann-type measured data
    • Authors: Alemdar Hasanov; Balgaisha Mukanova
      Abstract: Publication date: Available online 13 September 2016
      Source:Applied Numerical Mathematics
      Author(s): Alemdar Hasanov, Balgaisha Mukanova
      Inverse problem of identifying the unknown spacewise dependent source F ( x ) in 1D wave equation u t t = c 2 u x x + F ( x ) G ( t ) + h ( x , t ) , ( x , t ) ∈ ( 0 , 1 ) × ( 0 , T ) , from the Neumann-type measured output g ( t ) : = u x ( 0 , t ) is investigated. Most studies have attempted to reconstruct an unknown spacewise dependent source F ( x ) from the final observation u T ( x ) : = u ( x , T ) . Since a boundary measured data is most feasible from an engineering viewpoint, the identification problem has wide applications, in particular, in electrical networks governed by harmonically varying source for the linear wave equation u t t − u x x = F ( x ) c o s ( ω t ) , where ω > 0 is the frequency and F ( x ) is an unknown source term. In this paper Fourier Collocation Algorithm for reconstructing the spacewise dependent source F ( x ) is developed. This algorithm is based on Fourier expansion of the direct problem solution applied to the minimization problem for Tikhonov functional, by taking then a partial N-sum of the Fourier expansion. Tikhonov regularization is then applied to the obtained discrete ill-posed problem. To obtain high quality reconstruction in large values of the noise level, a numerical filtering algorithm is used for smoothing the noisy data. As an application, we demonstrate the ability of the algorithm on benchmark problems, in particular, on source identification problem in electrical networks governed by mono-frequency source. Numerical results show that the proposed algorithm allows to reconstruct the spacewise dependent source F ( x ) with enough high accuracy, in the presence of high noise levels.

      PubDate: 2016-09-20T15:29:25Z
       
  • The computation of the degree of an approximate greatest common divisor of
           two Bernstein polynomials
    • Authors: Martin Bourne; Joab Winkler
      Abstract: Publication date: Available online 6 September 2016
      Source:Applied Numerical Mathematics
      Author(s): Martin Bourne, Joab R. Winkler, Su Yi
      This paper considers the computation of the degree t of an approximate greatest common divisor d ( y ) of two Bernstein polynomials f ( y ) and g ( y ) , which are of degrees m and n respectively. The value of t is computed from the QR decomposition of the Sylvester resultant matrix S ( f , g ) and its subresultant matrices S k ( f , g ) , k = 2 , … , min ⁡ ( m , n ) , where S 1 ( f , g ) = S ( f , g ) . It is shown that the computation of t is significantly more complicated than its equivalent for two power basis polynomials because (a) S k ( f , g ) can be written in several forms that differ in the complexity of the computation of their entries, (b) different forms of S k ( f , g ) may yield different values of t, and (c) the binomial terms in the entries of S k ( f , g ) may cause the ratio of its entry of maximum magnitude to its entry of minimum magnitude to be large, which may lead to numerical problems. It is shown that the QR decomposition and singular value decomposition (SVD) of the Sylvester matrix and its subresultant matrices yield better results than the SVD of the Bézout matrix, and that f ( y ) and g ( y ) must be processed before computations are performed on these resultant and subresultant matrices in order to obtain good results.

      PubDate: 2016-09-09T16:28:07Z
       
 
 
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