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COMPUTER SCIENCE (1159 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: 13)
Abakós     Open Access   (Followers: 4)
ACM Computing Surveys     Hybrid Journal   (Followers: 23)
ACM Journal on Computing and Cultural Heritage     Hybrid Journal   (Followers: 9)
ACM Journal on Emerging Technologies in Computing Systems     Hybrid Journal   (Followers: 13)
ACM Transactions on Accessible Computing (TACCESS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Applied Perception (TAP)     Hybrid Journal   (Followers: 6)
ACM Transactions on Architecture and Code Optimization (TACO)     Hybrid Journal   (Followers: 9)
ACM Transactions on Autonomous and Adaptive Systems (TAAS)     Hybrid Journal   (Followers: 7)
ACM Transactions on Computation Theory (TOCT)     Hybrid Journal   (Followers: 12)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Computer Systems (TOCS)     Hybrid Journal   (Followers: 18)
ACM Transactions on Computer-Human Interaction     Hybrid Journal   (Followers: 14)
ACM Transactions on Computing Education (TOCE)     Hybrid Journal   (Followers: 5)
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: 21)
ACM Transactions on Intelligent Systems and Technology (TIST)     Hybrid Journal   (Followers: 8)
ACM Transactions on Interactive Intelligent Systems (TiiS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)     Hybrid Journal   (Followers: 10)
ACM Transactions on Reconfigurable Technology and Systems (TRETS)     Hybrid Journal   (Followers: 7)
ACM Transactions on Sensor Networks (TOSN)     Hybrid Journal   (Followers: 9)
ACM Transactions on Speech and Language Processing (TSLP)     Hybrid Journal   (Followers: 11)
ACM Transactions on Storage     Hybrid Journal  
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 25)
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: 11)
Advanced Engineering Materials     Hybrid Journal   (Followers: 26)
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Adaptive Data Analysis     Hybrid Journal   (Followers: 8)
Advances in Artificial Intelligence     Open Access   (Followers: 16)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Computer Science : an International Journal     Open Access   (Followers: 14)
Advances in Computing     Open Access   (Followers: 2)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 51)
Advances in Engineering Software     Hybrid Journal   (Followers: 26)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Human Factors/Ergonomics     Full-text available via subscription   (Followers: 26)
Advances in Human-Computer Interaction     Open Access   (Followers: 20)
Advances in Materials Sciences     Open Access   (Followers: 16)
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: 39)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Advances in Technology Innovation     Open Access   (Followers: 2)
AEU - International Journal of Electronics and Communications     Hybrid Journal   (Followers: 8)
African Journal of Information and Communication     Open Access   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Air, Soil & Water Research     Open Access   (Followers: 9)
AIS Transactions on Human-Computer Interaction     Open Access   (Followers: 6)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1)
Algorithms     Open Access   (Followers: 11)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
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: 4)
Anais da Academia Brasileira de Ciências     Open Access   (Followers: 2)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 7)
Analysis in Theory and Applications     Hybrid Journal   (Followers: 1)
Animation Practice, Process & Production     Hybrid Journal   (Followers: 5)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 7)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of Software Engineering     Hybrid Journal   (Followers: 13)
Annual Reviews in Control     Hybrid Journal   (Followers: 6)
Anuario Americanista Europeo     Open Access  
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: 14)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Clinical Informatics     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Computer Systems     Open Access   (Followers: 1)
Applied Informatics     Open Access  
Applied Mathematics and Computation     Hybrid Journal   (Followers: 33)
Applied Medical Informatics     Open Access   (Followers: 11)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Soft Computing     Hybrid Journal   (Followers: 16)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Architectural Theory Review     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives and Museum Informatics     Hybrid Journal   (Followers: 135)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Artifact     Hybrid Journal   (Followers: 2)
Artificial Life     Hybrid Journal   (Followers: 7)
Asia Pacific Journal on Computational Engineering     Open Access  
Asia-Pacific Journal of Information Technology and Multimedia     Open Access   (Followers: 1)
Asian Journal of Computer Science and Information Technology     Open Access  
Asian Journal of Control     Hybrid Journal  
Assembly Automation     Hybrid Journal   (Followers: 2)
at - Automatisierungstechnik     Hybrid Journal   (Followers: 1)
Australian Educational Computing     Open Access   (Followers: 1)
Automatic Control and Computer Sciences     Hybrid Journal   (Followers: 4)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Automatica     Hybrid Journal   (Followers: 11)
Automation in Construction     Hybrid Journal   (Followers: 6)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 8)
Basin Research     Hybrid Journal   (Followers: 5)
Behaviour & Information Technology     Hybrid Journal   (Followers: 52)
Biodiversity Information Science and Standards     Open Access  
Bioinformatics     Hybrid Journal   (Followers: 279)
Biomedical Engineering     Hybrid Journal   (Followers: 16)
Biomedical Engineering and Computational Biology     Open Access   (Followers: 14)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (Followers: 17)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (Followers: 33)
Briefings in Bioinformatics     Hybrid Journal   (Followers: 44)
British Journal of Educational Technology     Hybrid Journal   (Followers: 128)
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 10)
c't Magazin fuer Computertechnik     Full-text available via subscription   (Followers: 2)
CALCOLO     Hybrid Journal  
Calphad     Hybrid Journal  
Canadian Journal of Electrical and Computer Engineering     Full-text available via subscription   (Followers: 14)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 1)
Cell Communication and Signaling     Open Access   (Followers: 1)
Central European Journal of Computer Science     Hybrid Journal   (Followers: 5)
CERN IdeaSquare Journal of Experimental Innovation     Open Access  
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
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: 12)
Circuits and Systems     Open Access   (Followers: 16)
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: 20)
Communications Engineer     Hybrid Journal   (Followers: 1)
Communications in Algebra     Hybrid Journal   (Followers: 3)
Communications in Partial Differential Equations     Hybrid Journal   (Followers: 3)
Communications of the ACM     Full-text available via subscription   (Followers: 54)
Communications of the Association for Information Systems     Open Access   (Followers: 18)
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering     Hybrid Journal   (Followers: 3)
Complex & Intelligent Systems     Open Access  
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: 2)
Computational and Theoretical Chemistry     Hybrid Journal   (Followers: 9)
Computational Astrophysics and Cosmology     Open Access   (Followers: 1)
Computational Biology and Chemistry     Hybrid Journal   (Followers: 12)
Computational Chemistry     Open Access   (Followers: 2)
Computational Cognitive Science     Open Access   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Condensed Matter     Open Access  
Computational Ecology and Software     Open Access   (Followers: 9)
Computational Economics     Hybrid Journal   (Followers: 9)
Computational Geosciences     Hybrid Journal   (Followers: 15)
Computational Linguistics     Open Access   (Followers: 23)
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: 2)
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: 13)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 31)
Computer     Full-text available via subscription   (Followers: 87)
Computer Aided Surgery     Hybrid Journal   (Followers: 3)
Computer Applications in Engineering Education     Hybrid Journal   (Followers: 7)
Computer Communications     Hybrid Journal   (Followers: 10)
Computer Engineering and Applications Journal     Open Access   (Followers: 5)
Computer Journal     Hybrid Journal   (Followers: 8)
Computer Methods in Applied Mechanics and Engineering     Hybrid Journal   (Followers: 21)
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: 16)
Computer Physics Communications     Hybrid Journal   (Followers: 6)
Computer Science - Research and Development     Hybrid Journal   (Followers: 7)
Computer Science and Engineering     Open Access   (Followers: 17)
Computer Science and Information Technology     Open Access   (Followers: 12)
Computer Science Education     Hybrid Journal   (Followers: 13)
Computer Science Journal     Open Access   (Followers: 20)
Computer Science Master Research     Open Access   (Followers: 10)

        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  [3049 journals]
  • Parameter selection for HOTV regularization
    • Authors: Toby Sanders
      Pages: 1 - 9
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Toby Sanders
      Popular methods for finding regularized solutions to inverse problems include sparsity promoting ℓ 1 regularization techniques, one in particular which is the well known total variation (TV) regularization. More recently, several higher order (HO) methods similar to TV have been proposed, which we generally refer to as HOTV methods. In this letter, we investigate the problem of the often debated selection of λ, the parameter used to carefully balance the interplay between data fitting and regularization terms. We theoretically argue for a scaling of the operators for a uniform parameter selection for all orders of HOTV regularization. In particular, parameter selection for all orders of HOTV may be determined by scaling an initial parameter for TV, which the imaging community may be more familiar with. We also provide several numerical results which justify our theoretical findings.

      PubDate: 2017-11-09T09:57:16Z
      DOI: 10.1016/j.apnum.2017.10.010
      Issue No: Vol. 125 (2017)
  • A pseudospectral scheme and its convergence analysis for high-order
           integro-differential equations
    • Authors: Xiaojun Tang; Heyong Xu
      Pages: 51 - 67
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Xiaojun Tang, Heyong Xu
      The main purpose of this work is to develop an integral pseudospectral scheme for solving integro-differential equations. We provide new pseudospectral integration matrices (PIMs) for the Legendre–Gauss and the flipped Legendre–Gauss–Radau points, respectively, and present an efficient and stable approach to computing the PIMs via the recursive calculation of Legendre integration matrices. Furthermore, we provide a rigorous convergence analysis for the proposed pseudospectral scheme in both L ∞ and L 2 spaces via a linear integral equation, and the spectral rate of convergence is demonstrated by numerical results.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.003
      Issue No: Vol. 125 (2017)
  • Fast computation of stationary joint probability distribution of sparse
           Markov chains
    • Authors: Weiyang Ding; Michael Ng; Yimin Wei
      Pages: 68 - 85
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Weiyang Ding, Michael Ng, Yimin Wei
      In this paper, we study a fast algorithm for finding stationary joint probability distributions of sparse Markov chains or multilinear PageRank vectors which arise from data mining applications. In these applications, the main computational problem is to calculate and store solutions of many unknowns in joint probability distributions of sparse Markov chains. Our idea is to approximate large-scale solutions of such sparse Markov chains by two components: the sparsity component and the rank-one component. Here the non-zero locations in the sparsity component refer to important associations in the joint probability distribution and the rank-one component refers to a background value of the solution. We propose to determine solutions by formulating and solving sparse and rank-one optimization problems via closed form solutions. The convergence of the truncated power method is established. Numerical examples of multilinear PageRank vector calculation and second-order web-linkage analysis are presented to show the efficiency of the proposed method. It is shown that both computation and storage are significantly reduced by comparing with the traditional power method.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.008
      Issue No: Vol. 125 (2017)
  • Conforming finite element methods for the stochastic
           Cahn–Hilliard–Cook equation
    • Authors: Shimin Chai; Yanzhao Cao; Yongkui Zou; Wenju Zhao
      Pages: 44 - 56
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): Shimin Chai, Yanzhao Cao, Yongkui Zou, Wenju Zhao
      This paper is concerned with the finite element approximation of the stochastic Cahn–Hilliard–Cook equation driven by an infinite dimensional Wiener type noise. The Argyris finite elements are used to discretize the spatial variables while the infinite dimensional (cylindrical) Wiener process is approximated by truncated stochastic series spanned by the spectral basis of the covariance operator. The optimal strong convergence order in L 2 and H ˙ − 2 norms is obtained. Unlike the mixed finite element method studied in the existing literature, our method allows the covariance operator of the Wiener process to have an infinite trace, including the space–time white noise is allowed in our model. Numerical experiments are presented to illustrate the theoretical analysis.

      PubDate: 2017-10-25T12:06:02Z
      DOI: 10.1016/j.apnum.2017.09.010
      Issue No: Vol. 124 (2017)
  • A high-order fully conservative block-centered finite difference method
           for the time-fractional advection–dispersion equation
    • Authors: Xiaoli Li; Hongxing Rui
      Pages: 89 - 109
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): Xiaoli Li, Hongxing Rui
      Based on the weighted and shifted Grünwald–Letnikov difference operator, a new high-order block-centered finite difference method is derived for the time-fractional advection–dispersion equation by introducing an auxiliary flux variable to guarantee full mass conservation. The stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with optimal order of convergence O ( Δ t 3 + h 2 + k 2 ) both for solute concentration and the auxiliary flux variable are established on non-uniform rectangular grids, where Δ t ,   h and k are the step sizes in time, space in x- and y-direction. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.004
      Issue No: Vol. 124 (2017)
  • The fictitious domain method with H1-penalty for the Stokes problem with
           Dirichlet boundary condition
    • Authors: Guanyu Zhou
      Pages: 1 - 21
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Guanyu Zhou
      We consider the fictitious domain method with H 1 -penalty for the Stokes problem with Dirichlet boundary condition. First, for the continuous penalty problem, we obtain the optimal error estimate O ( ϵ ) for both the velocity and pressure, where ϵ is the penalty parameter. Moreover, we investigate the H m -regularity for the solution of the penalty problem. Then, we apply the finite element method with the P1/P1 element to the penalty problem. Since the solution to the penalty problem has a jump in the traction vector, we introduce some interpolation/projection operators, as well as an inf-sup condition with the norm depending on ϵ. With the help of these preliminaries, we derive the error estimates for the finite element approximation. The theoretical results are verified by the numerical experiments.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.005
      Issue No: Vol. 123 (2017)
  • Implicit–Explicit WENO scheme for the equilibrium dispersive model
           of chromatography
    • Authors: R. Donat; F. Guerrero; P. Mulet
      Pages: 22 - 42
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): R. Donat, F. Guerrero, P. Mulet
      Chromatographic processes can be modeled by nonlinear, convection-dominated partial differential equations, together with nonlinear relations: the adsorption isotherms. In this paper we consider the nonlinear equilibrium dispersive (ED) model with adsorption isotherms of Langmuir type. We show that, in this case, the ED model can be written as a system of conservation laws when the dispersion coefficient vanishes. We also show that the function that relates the conserved variables and the physically observed concentrations of the components in the mixture is one to one and it admits a global inverse, which cannot be given explicitly, but can be adequately computed. As a result, fully conservative numerical schemes can be designed for the ED model in chromatography. We propose a Weighted-Essentially-non-Oscillatory second order IMEX scheme and describe the numerical issues involved in its application. Through a series of numerical experiments, we show that our scheme gives accurate numerical solutions which capture the sharp discontinuities present in the chromatographic fronts, with the same stability restrictions as in the purely hyperbolic case.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.008
      Issue No: Vol. 123 (2017)
  • Fractional PDE constrained optimization: An optimize-then-discretize
           approach with L-BFGS and approximate inverse preconditioning
    • Authors: Stefano Cipolla; Fabio Durastante
      Pages: 43 - 57
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Stefano Cipolla, Fabio Durastante
      In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation. Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver. A suitable preconditioning strategy by approximate inverses is taken into account. Graphics Processing Unit (GPU) accelerator is used in the construction of the preconditioners. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.09.001
      Issue No: Vol. 123 (2017)
  • Algorithms for the implementation of adaptive isogeometric methods using
           hierarchical B-splines
    • Authors: Eduardo M. Garau; Rafael Vázquez
      Pages: 58 - 87
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Eduardo M. Garau, Rafael Vázquez
      In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and coarsening that, unlike previously existing methods, can be understood as the inverse of each other. We also define simple and intuitive data structures for the implementation of hierarchical B-splines, and algorithms for refinement and coarsening that take advantage of local information. We complete the paper with some simple numerical tests to show the performance of the data structures and algorithms, that have been implemented in the open-source Octave/Matlab code GeoPDEs.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.006
      Issue No: Vol. 123 (2017)
  • Supercloseness of the continuous interior penalty method for singularly
           perturbed problems in 1D: Vertex-cell interpolation
    • Authors: Jin Zhang; Xiaowei Liu
      Pages: 88 - 98
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Jin Zhang, Xiaowei Liu
      A continuous interior penalty method with piecewise polynomials of degree p ≥ 2 is applied on a Shishkin mesh to solve a singularly perturbed convection–diffusion problem, whose solution has a single boundary layer. This method is analyzed by means of a series of integral identities developed for the convection terms. Then we prove a supercloseness bound of order 5/2 for a vertex-cell interpolation when p = 2 . The sharpness of our analysis is supported by some numerical experiments. Moreover, numerical tests show supercloseness clearly for p ≥ 3 .

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.09.003
      Issue No: Vol. 123 (2017)
  • Fully spectral collocation method for nonlinear parabolic partial
           integro-differential equations
    • Authors: Farhad Fakhar-Izadi; Mehdi Dehghan
      Pages: 99 - 120
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Farhad Fakhar-Izadi, Mehdi Dehghan
      The numerical approximation of solution to nonlinear parabolic Volterra and Fredholm partial integro-differential equations is studied in this paper. Unlike the conventional methods which discretize the time variable by finite difference schemes, we use the spectral method for this purpose. Indeed, both of the space and time discretizations are based on the Legendre-collocation method which lead to conversion of the problem to a nonlinear system of algebraic equations. The convergence of the proposed method is proven by providing an L ∞ error estimate. Several numerical examples are included to demonstrate the efficiency and spectral accuracy of the proposed method in the space and time directions.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.08.007
      Issue No: Vol. 123 (2017)
  • Solving a class of nonlinear boundary integral equations based on the
           meshless local discrete Galerkin (MLDG) method
    • Authors: Pouria Assari; Mehdi Dehghan
      Pages: 137 - 158
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Pouria Assari, Mehdi Dehghan
      The main purpose of this article is to investigate a computational scheme for solving a class of nonlinear boundary integral equations which occurs as a reformulation of boundary value problems of Laplace's equations with nonlinear Robin boundary conditions. The method approximates the solution by the Galerkin method based on the use of moving least squares (MLS) approach as a locally weighted least square polynomial fitting. The discrete Galerkin method for solving boundary integral equations results from the numerical integration of all integrals appeared in the method. The numerical scheme developed in the current paper utilizes the non-uniform Gauss–Legendre quadrature rule to estimate logarithm-like singular integrals. Since the proposed method is constructed on a set of scattered points, it does not require any background mesh and so we can call it as the meshless local discrete Galerkin (MLDG) method. The scheme is simple and effective to solve boundary integral equations and its algorithm can be easily implemented. We also obtain the error bound and the convergence rate of the presented method. Finally, numerical examples are included to show the validity and efficiency of the new technique and confirm the theoretical error estimates.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.002
      Issue No: Vol. 123 (2017)
  • On order conditions for modified Patankar–Runge–Kutta schemes
    • Authors: S. Kopecz; A. Meister
      Pages: 159 - 179
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): S. Kopecz, A. Meister
      In [6] the modified Patankar–Euler and modified Patankar–Runge–Kutta schemes were introduced to solve positive and conservative systems of ordinary differential equations. These modifications of the forward Euler scheme and Heun's method guarantee positivity and conservation irrespective of the chosen time step size. In this paper we introduce a general definition of modified Patankar–Runge–Kutta schemes and derive necessary and sufficient conditions to obtain first and second order methods. We also introduce two novel families of two-stage second order modified Patankar–Runge–Kutta schemes.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.004
      Issue No: Vol. 123 (2017)
  • Weak Galerkin mixed finite element method for heat equation
    • Authors: Chenguang Zhou; Yongkui Zou; Shimin Chai; Qian Zhang; Hongze Zhu
      Pages: 180 - 199
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Chenguang Zhou, Yongkui Zou, Shimin Chai, Qian Zhang, Hongze Zhu
      In this paper, we apply a new weak Galerkin mixed finite element method (WGMFEM) with stabilization term to solve heat equations. This method allows the usage of totally discontinuous functions in the approximation space. The WGMFEM is capable of providing very accurate numerical approximations for both the primary and flux variables. In addition, we develop and analyze the error estimates for both continuous and discontinuous time WGMFEM schemes. Optimal order error estimates in both L 2 and triple-bar ⫼ ⋅ ⫼ norms are established, respectively. Finally, numerical tests are conducted to illustrate the theoretical results.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.08.009
      Issue No: Vol. 123 (2017)
  • On the partial condition numbers for the indefinite least squares problem
    • Authors: Hanyu Li; Shaoxin Wang
      Pages: 200 - 220
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Hanyu Li, Shaoxin Wang
      The condition number of a linear function of the indefinite least squares solution is called the partial condition number for the indefinite least squares problem. In this paper, based on a new and very general condition number which can be called the unified condition number, we first present an expression of the partial unified condition number when the data space is measured by a general weighted product norm. Then, by setting the specific norms and weight parameters, we obtain the expressions of the partial normwise, mixed and componentwise condition numbers. Moreover, the corresponding structured partial condition numbers are also taken into consideration when the problem is structured. Considering the connections between the indefinite and total least squares problems, we derive the (structured) partial condition numbers for the latter, which generalize the ones in the literature. To estimate these condition numbers effectively and reliably, the probabilistic spectral norm estimator and the small-sample statistical condition estimation method are applied and three related algorithms are devised. Finally, the obtained results are illustrated by numerical experiments.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.006
      Issue No: Vol. 123 (2017)
  • Numerical simulation of Bloch equations for dynamic magnetic resonance
    • Authors: Arijit Hazra; Gert Lube; Hans-Georg Raumer
      Pages: 241 - 255
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Arijit Hazra, Gert Lube, Hans-Georg Raumer
      Magnetic Resonance Imaging (MRI) is a widely applied non-invasive imaging modality based on non-ionizing radiation which gives excellent images and soft tissue contrast of living tissues. We consider the modified Bloch problem as a model of MRI for flowing spins in an incompressible flow field. After establishing the well-posedness of the corresponding evolution problem, we analyze its spatial semi-discretization using discontinuous Galerkin methods. The high frequency time evolution requires a proper explicit and adaptive temporal discretization. The applicability of the approach is shown for basic examples.

      PubDate: 2017-10-11T14:37:22Z
      DOI: 10.1016/j.apnum.2017.09.007
      Issue No: Vol. 123 (2017)
  • Analysis of a velocity–stress–pressure formulation for a
           fluid–structure interaction problem
    • Authors: María González; Virginia Selgas
      Pages: 275 - 299
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): María González, Virginia Selgas
      We consider a fluid–structure interaction problem consisting of the time-dependent Stokes equations in the fluid domain coupled with the equations of linear elastodynamics in the solid domain. For simplicity, all changes of geometry are neglected. We propose a new method in terms of the fluid velocity, the fluid pressure, the structural velocity and the Cauchy stress tensor. We show that the new weak formulation is well-posed. Then, we propose a new semidiscrete problem where the velocities and the fluid pressure are approximated using a stable pair for the Stokes problem in the fluid domain and compatible finite elements in the solid domain. We obtain a priori estimates for the solution of the semidiscrete problem, prove the convergence of these solutions to the solution of the weak formulation and obtain error estimates. A time discretization based on the backward Euler method leads to a fully discrete scheme in which the computation of the approximated Cauchy stress tensor can be decoupled from that of the remaining unknowns at each time step. The displacements in the structure (if needed) can be recovered by quadrature. Finally, some numerical experiments showing the performance of the method are provided.

      PubDate: 2017-10-11T14:37:22Z
      DOI: 10.1016/j.apnum.2017.09.011
      Issue No: Vol. 123 (2017)
  • A lagged diffusivity method for reaction–convection–diffusion
           equations with Dirichlet boundary conditions
    • Authors: Francesco Mezzadri; Emanuele Galligani
      Pages: 300 - 319
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Francesco Mezzadri, Emanuele Galligani
      In this paper we solve a 2D nonlinear, non-steady reaction–convection–diffusion equation subject to Dirichlet boundary conditions by an iterative procedure consisting in lagging the diffusion term. First, we analyze the procedure, which we call Lagged Diffusivity Method. In particular, we provide a proof of the uniqueness of the solution and of the convergence of the lagged iteration when some assumptions are satisfied. We also describe outer and inner solvers, with special regard to how to link the stopping criteria in an efficient way. Numerical experiments are then introduced in order to evaluate the role of different linear solvers and of other components of the solution procedure, considering also the effect of the discretization.

      PubDate: 2017-10-11T14:37:22Z
      DOI: 10.1016/j.apnum.2017.09.009
      Issue No: Vol. 123 (2017)
  • A posteriori error estimates and adaptivity for the discontinuous Galerkin
           solutions of nonlinear second-order initial-value problems
    • Authors: Mahboub Baccouch
      Pages: 18 - 37
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Mahboub Baccouch
      In this paper, we propose and analyze an efficient and reliable a posteriori error estimator of residual-type for the discontinuous Galerkin (DG) method applied to nonlinear second-order initial-value problems for ordinary differential equations. This estimator is simple, efficient, and asymptotically exact. We use our recent optimal L 2 error estimates and superconvergence results of Baccouch [15] to show that the significant parts of the DG discretization errors are proportional to the ( p + 1 ) -degree right Radau polynomial, when polynomials of total degree not exceeding p are used. These new results allow us to construct a residual-based a posteriori error estimator which is obtained by solving a local residual problem with no initial condition on each element. We prove that, for smooth solutions, the proposed a posteriori error estimator converges to the actual error in the L 2 -norm with order of convergence p + 2 . Computational results indicate that the theoretical order of convergence is sharp. By adding the a posteriori error estimate to the DG solution, we obtain a post-processed approximation which superconverges with order p + 2 in the L 2 -norm. Moreover, we demonstrate the effectiveness of the this error estimator. Finally, we present a local adaptive mesh refinement (AMR) procedure that makes use of our local a posteriori error estimate. Our proofs are valid for arbitrary regular meshes and for P p polynomials with p ≥ 1 . Several numerical results are presented to validate the theoretical results.

      PubDate: 2017-07-02T16:25:43Z
      DOI: 10.1016/j.apnum.2017.06.001
      Issue No: Vol. 121 (2017)
  • Uncertainty quantification for linear hyperbolic equations with stochastic
           process or random field coefficients
    • Authors: Andrea Barth; Franz G. Fuchs
      Pages: 38 - 51
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Andrea Barth, Franz G. Fuchs
      In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein–Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.

      PubDate: 2017-07-12T12:47:24Z
      DOI: 10.1016/j.apnum.2017.06.009
      Issue No: Vol. 121 (2017)
  • A double-sided dynamic programming approach to the minimum time problem
           and its numerical approximation
    • Authors: Lars Grüne; Thuy T.T. Le
      Pages: 68 - 81
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Lars Grüne, Thuy T.T. Le
      We introduce a new formulation of the minimum time problem in which we employ the signed minimum time function positive outside of the target, negative in its interior and zero on its boundary. Under some standard assumptions, we prove the so called Bridge Dynamic Programming Principle (BDPP) which is a relation between the value functions defined on the complement of the target and in its interior. Then owing to BDPP, we obtain the error estimates of a semi-Lagrangian discretization of the resulting Hamilton–Jacobi–Bellman equation. In the end, we provide numerical tests and error comparisons which show that the new approach can lead to significantly reduced numerical errors.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.008
      Issue No: Vol. 121 (2017)
  • A new Crank–Nicolson finite element method for the time-fractional
           subdiffusion equation
    • Authors: Fanhai Zeng; Changpin Li
      Pages: 82 - 95
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Fanhai Zeng, Changpin Li
      In this paper, a new Crank–Nicolson finite element method for the time-fractional subdiffusion equation is developed, in which a novel time discretization called the modified L1 method is used to discretize the Riemann–Liouville fractional derivative. The present method is unconditionally stable and convergent of order O ( τ 1 + β + h r + 1 ) , where β ∈ ( 0 , 1 ) , τ and h are the step sizes in time and space, respectively, and r is the degree of the piecewise polynomial space. The derived method is reduced to the classical Crank–Nicolson method when β → 1 . The new time discretization is also used to solve the fractional cable equation. And the unconditional stability and convergence are given. Numerical examples are provided which support the theoretical analysis. The comparison with the existing methods are also given, which shows good performances of the present methods.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.011
      Issue No: Vol. 121 (2017)
  • Curvature-induced instability of a Stokes-like problem with non-standard
           boundary conditions
    • Authors: Armin Westerkamp; Manuel Torrilhon
      Pages: 96 - 114
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Armin Westerkamp, Manuel Torrilhon
      We present an analysis of a set of parametrized boundary conditions for a Stokes–Brinkman model in two space dimensions, discretized by finite elements. We particularly point out an instability which arises when these boundary conditions are posed on a curved line, which then leads to unphysical oscillations. In contrast to a Navier-slip condition, which is prone to Babuška's paradox, this instability can be traced back to the continuous level. We claim that the stability in these cases depend on the amount of curvature at the boundary, which is shown in a reduced setting in cylinder coordinates. The transition to a two dimensional Cartesian case is then based on numerical studies, which further substantiate the claim. Lastly, stabilization techniques are motivated that enhance the continuous FEM setting and are conveniently able to deal with arising oscillations.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.012
      Issue No: Vol. 121 (2017)
  • Second order accurate asynchronous scheme for modeling linear partial
           differential equations
    • Authors: Asma Toumi; Guillaume Dufour; Ronan Perrussel; Thomas Unfer
      Pages: 115 - 133
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Asma Toumi, Guillaume Dufour, Ronan Perrussel, Thomas Unfer
      We propose an asynchronous method for the explicit integration of multi-scale partial differential equations. This method is restricted by a local CFL (Courant Friedrichs Lewy) condition rather than the traditional global CFL condition. Moreover, contrary to other local time-stepping (LTS) methods, the asynchronous algorithm permits the selection of independent time steps in each mesh element. We derived an asynchronous Runge–Kutta 2 (ARK2) scheme from a standard explicit Runge–Kutta method and we proved that the ARK2 scheme is second order convergent. Comparing with the classical integration, the asynchronous scheme is effective in terms of computation time.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.014
      Issue No: Vol. 121 (2017)
  • A numerical method for solving some model problems arising in science and
           convergence analysis based on residual function
    • Authors: Ömür Kıvanç Kürkçü; Ersin Aslan; Mehmet Sezer
      Pages: 134 - 148
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Ömür Kıvanç Kürkçü, Ersin Aslan, Mehmet Sezer
      In this study, we solve some widely-used model problems consisting of linear, nonlinear differential and integral equations, employing Dickson polynomials with the parameter-α and the collocation points for an efficient matrix method. The convergence of a Dickson polynomial solution of the model problem is investigated by means of the residual function. We encode useful computer programs for model problems, in order to obtain the precise Dickson polynomial solutions. These solutions are plotted along with the exact solutions in figures and the numerical results are compared with other well-known methods in tables.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.015
      Issue No: Vol. 121 (2017)
  • An adaptive Galerkin method for the time-dependent complex
           Schrödinger equation
    • Authors: A.I. Ávila; A. Meister; M. Steigemann
      Pages: 149 - 169
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): A.I. Ávila, A. Meister, M. Steigemann
      Nonlinear time-dependent Schrödinger equations (NLSE) model several important problems in quantum physics and morphogenesis. Recently, vortex lattice formation were experimentally found in Bose–Einstein condensate and Fermi superfluids, which are modeled by adding a rotational term in the NLSE equation. Numerical solutions have been computed by using separate approaches for time and space variables. If we see the complex equation as a system, wave methods can be used. In this article, we consider finite element approximations using continuous Galerkin schemes in time and space by adaptive mesh balancing both errors. To get this balance, we adapt the dual weighted residual method used for wave equations and estimates of error indicators for adaptive space–time finite element discretization. The results show how important is dynamic refinement to control the degrees of freedom in space.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.06.013
      Issue No: Vol. 121 (2017)
  • Nonsmooth data error estimates for FEM approximations of the time
           fractional cable equation
    • Authors: Peng Zhu; Shenglan Xie; Xiaoshen Wang
      Pages: 170 - 184
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Peng Zhu, Shenglan Xie, Xiaoshen Wang
      In this paper, the fractional cable equation, involving two Riemann–Liouville fractional derivatives, with initial/boundary condition is considered. Two fully discrete schemes are obtained by employing piecewise linear Galerkin FEM in space, and using convolution quadrature methods based on the first- and second-order backward difference methods in time. Optimal error estimates in terms of the initial data and the inhomogeneity for the semi-discrete scheme and fully discrete schemes are discussed. Numerical results are shown to verify the theoretical results.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.07.005
      Issue No: Vol. 121 (2017)
  • Fast and exact 2d image reconstruction based on Hakopian interpolation
    • Authors: Xuenan Sun; Xuezhang Liang
      Pages: 185 - 197
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Xuenan Sun, Xuezhang Liang
      A new algorithm for the reconstruction of two-dimensional (2D) images from projections is given. The algorithm is based on the expansions of Hakopian interpolation polynomial into Chebyshev–Fourier series. The computer simulation experiments show that the new algorithm is effective.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.07.002
      Issue No: Vol. 121 (2017)
  • Novel alternating update method for low rank approximation of structured
    • Authors: Jianchao Bai; Jicheng Li; Pingfan Dai
      Pages: 223 - 233
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Jianchao Bai, Jicheng Li, Pingfan Dai
      This work is devoted to designing a unified alternating update method for solving a class of structured low rank approximations under the convex and unitarily invariant norm. By the aid of the variational inequality and monotone operator, the proposed method is proved to converge to the solution point of an equivalent variational inequality with a worst-case O ( 1 / t ) convergence rate in a nonergodic sense. We also analyze that the involved subproblems under the Frobenius norm are respectively equivalent to the structured least-squares problem and low rank least-squares problem, where the explicit solutions to some special cases are derived. In order to investigate the efficiency of the proposed method, several examples in system identification are tested to validate that the proposed method can outperform some state-of-the-art methods.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.07.001
      Issue No: Vol. 121 (2017)
  • Construction of IMEX DIMSIMs of high order and stage order
    • Authors: Z. Jackiewicz; H. Mittelmann
      Pages: 234 - 248
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Z. Jackiewicz, H. Mittelmann
      For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit–explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by implicit formula, and the non-stiff part is integrated by an explicit formula. We analyze stability of these methods when the implicit and explicit parts interact with each other. We look for methods with large absolute stability region, assuming that the implicit part of the method is A ( α ) -, A-, or L-stable. Finally, we furnish examples of IMEX DIMSIMs of order p = 5 and p = 6 and stage order q = p , with good stability properties. Numerical examples illustrate that the IMEX schemes constructed in this paper do not suffer from order reduction phenomenon for some range of stepsizes.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.07.004
      Issue No: Vol. 121 (2017)
  • Mixed recurrence equations and interlacing properties for zeros of
           sequences of classical q-orthogonal polynomials
    • Authors: D.D. Tcheutia; A.S. Jooste; W. Koepf
      Abstract: Publication date: Available online 14 November 2017
      Source:Applied Numerical Mathematics
      Author(s): D.D. Tcheutia, A.S. Jooste, W. Koepf
      Using the q-version of Zeilberger's algorithm, we provide a procedure to find mixed recurrence equations satisfied by classical q-orthogonal polynomials with shifted parameters. These equations are used to investigate interlacing properties of zeros of sequences of q-orthogonal polynomials. In the cases where zeros do not interlace, we give some numerical examples to illustrate this.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.11.003
  • The Crank-Nicolson/Adams-Bashforth scheme for the Burgers equation with H2
           and H1 initial data
    • Authors: Tong Zhang; JiaoJiao Jin; YuGao HuangFu
      Abstract: Publication date: Available online 10 November 2017
      Source:Applied Numerical Mathematics
      Author(s): Tong Zhang, JiaoJiao Jin, YuGao HuangFu
      In this paper, we consider the stability and convergence results of the Crank-Nicolson/Adams-Bashforth scheme for the Burgers equation with smooth and nonsmooth initial data. The spatial approximation is based on the standard conforming finite element space. The temporal treatment of the spatial discrete Burgers equation is based on the implicit Crank-Nicolson scheme for the linear term and the explicit Adams-Bashforth scheme for the nonlinear term. Firstly, we prove that the Crank-Nicolson/Adams-Bashforth scheme is almost unconditionally stable with initial data u 0 ∈ H α ( α = 1 , 2 ) . Secondly, the optimal error estimates of the numerical solution in L 2 -norm are derived with initial data u 0 ∈ H 2 , and the error estimates of approximate solution in L 2 norm obtained with initial data u 0 ∈ H 1 is reduced by 1 2 . Finally, some numerical examples are provided to verify the established stability theory and convergence results with H 2 and H 1 initial data.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.009
  • The matrix splitting based proximal fixed-point algorithms for
           quadratically constrained ℓ1 minimization and Dantzig selector
    • Authors: Yongchao Yu; Jigen Peng
      Abstract: Publication date: Available online 3 November 2017
      Source:Applied Numerical Mathematics
      Author(s): Yongchao Yu, Jigen Peng
      This paper studies algorithms for solving quadratically constrained ℓ 1 minimization and Dantzig selector which have recently been widely used to tackle sparse recovery problems in compressive sensing. The two optimization models can be reformulated via two indicator functions as special cases of a general convex composite model which minimizes the sum of two convex functions with one composed with a matrix operator. The general model can be transformed into a fixed-point problem for a nonlinear operator which is composed of a proximity operator and an expansive matrix operator, and then a new iterative scheme based on the expansive matrix splitting is proposed to find fixed-points of the nonlinear operator. We also give some mild conditions to guarantee that the iterative sequence generated by the scheme converges to a fixed-point of the nonlinear operator. Further, two specific proximal fixed-point algorithms based on the scheme are developed and then applied to quadratically constrained ℓ 1 minimization and Dantzig selector. Numerical results have demonstrated that the proposed algorithms are comparable to the state-of-the-art algorithms for recovering sparse signals with different sizes and dynamic ranges in terms of both accuracy and speed. In addition, we also extend the proposed algorithms to solve two harder constrained total-variation minimization problems.

      PubDate: 2017-11-09T09:57:16Z
      DOI: 10.1016/j.apnum.2017.11.001
  • Splitting schemes for unsteady problems involving the grad-div operator
    • Authors: Peter Minev; Petr N. Vabishchevich
      Abstract: Publication date: Available online 31 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Peter Minev, Petr N. Vabishchevich
      In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the solution vector. In this paper we discuss various possibilities to decouple the equations for the different components that result in unconditionally stable schemes. If the spatial discretization uses Cartesian grids, the resulting schemes are Locally One Dimensional (LOD). The stability analysis of these schemes is based on the general stability theory of additive operator-difference schemes developed by Samarskii and his collaborators. The results of the theoretical analysis are illustrated on a 2D numerical example with a smooth manufactured solution.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.005
  • Mixed generalized Hermite-Fourier spectral method for Fokker-Planck
           equation of periodic field
    • Authors: Guo Chai; Tian-jun Wang
      Abstract: Publication date: Available online 31 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Guo Chai, Tian-jun Wang
      In this paper, we develop a mixed Hermite-Fourier spectral method for the Fokker-Planck equation of periodic field. Radical to the numerical solutions of partial differential equations of the sort, results on mixed generalized Hermite-Fourier orthogonal approximation are established. The convergence of the constructed spectral scheme is proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.006
  • Residual error estimation for anisotropic Kirchhoff plates
    • Authors: Michael Weise
      Abstract: Publication date: Available online 31 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Michael Weise
      Residual error estimation for conforming finite element discretisations of the isotropic Kirchhoff plate problem is covered by an estimator of Verfürth for the related biharmonic equation. This article generalises Verfürth's result to Kirchhoff plates with an anisotropic material, which requires some modifications. Special emphasis is laid on the reduced Hsieh–Clough–Tocher triangular finite element, the conforming element with the least possible number of unknowns.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.007
  • Differential equations for families of semi-classical orthogonal
           polynomials within class one
    • Authors: G. Filipuk; M.N. Rebocho
      Abstract: Publication date: Available online 23 October 2017
      Source:Applied Numerical Mathematics
      Author(s): G. Filipuk, M.N. Rebocho
      In this paper we study families of semi-classical orthogonal polynomials within class one. We derive general second or third order ordinary differential equations (with respect to certain parameters) for the recurrence coefficients of the three-term recurrence relation of these polynomials and show that in particular well-known cases, e.g. related to the modified Airy and Laguerre weights, these equations can be reduced to the second and the fourth Painlevé equations.

      PubDate: 2017-10-25T12:06:02Z
      DOI: 10.1016/j.apnum.2017.10.002
  • A new quadrature scheme based on an Extended Lagrange Interpolation
    • Authors: Donatella Occorsio; Maria Grazia Russo
      Abstract: Publication date: Available online 18 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Donatella Occorsio, Maria Grazia Russo
      Let w ( x ) = e − x β x α , w ¯ ( x ) = x w ( x ) and let { p m ( w ) } m , { p m ( w ¯ ) } m be the corresponding sequences of orthonormal polynomials. Since the zeros of p m + 1 ( w ) interlace those of p m ( w ¯ ) , it makes sense to construct an interpolation process essentially based on the zeros of Q 2 m + 1 : = p m + 1 ( w ) p m ( w ¯ ) , which is called “Extended Lagrange Interpolation". In this paper the convergence of this interpolation process is studied in suitable weighted L 1 spaces, in a general framework which completes the results given by the same authors in weighted L u p ( ( 0 , + ∞ ) ) , 1 ≤ p ≤ ∞ (see [30], [27]). As an application of the theoretical results, an extended product integration rule, based on the aforesaid Lagrange process, is proposed in order to compute integrals of the type ∫ 0 + ∞ f ( x ) k ( x , y ) u ( x ) d x , u ( x ) = e − x β x γ ( 1 + x ) λ , γ > − 1 , λ ∈ R + , where the kernel k ( x , y ) can be of different kinds. The rule, which is stable and fast convergent, is used in order to construct a computational scheme involving the single product integration rule studied in [22]. It is shown that the “compound quadrature sequence” represents an efficient proposal for saving 1/3 of the evaluations of the function f, under unchanged speed of convergence.
      PubDate: 2017-10-25T12:06:02Z
  • Stability and convergence analysis of a Crank-Nicolson leap-frog scheme
           for the unsteady incompressible Navier-Stokes equations
    • Authors: Qili Tang; Yunqing Huang
      Abstract: Publication date: Available online 12 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Qili Tang, Yunqing Huang
      A fully discrete Crank-Nicolson leap-frog (CNLF) scheme is presented and studied for the nonstationary incompressible Navier-Stokes equations. The proposed scheme deals with the spatial discretization by Galerkin finite element method (FEM), treats the temporal discretization by CNLF method for the linear term and the semi-implicit method for nonlinear term. The almost unconditional stability, i.e., the time step is no more than a constant, is proven. By a new negative norm technique, the L 2 -optimal error estimates with respect to temporal and spacial orientation for the velocity are derived. At last, some numerical results are provided to justify our theoretical analysis.

      PubDate: 2017-10-18T15:25:02Z
      DOI: 10.1016/j.apnum.2017.09.012
  • On the discretization and application of two space–time boundary
           integral equations for 3D wave propagation problems in unbounded domains
    • Authors: Falletta Monegato; Scuderi
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): S. Falletta, G. Monegato, L. Scuderi
      In this paper, we consider 3D wave propagation problems in unbounded domains, such as those of acoustic waves in non viscous fluids, or of seismic waves in (infinite) homogeneous isotropic materials, where the propagation velocity c is much higher than 1. For example, in the case of air and water c ≈ 343 m / s and c ≈ 1500 m / s respectively, while for seismic P-waves in linear solids we may have c ≈ 6000 m / s or higher. These waves can be generated by sources, possible away from the obstacles. We further assume that the dimensions of the obstacles are much smaller than that of the wave velocity, and that the problem transients are not excessively short. For their solution we consider two different approaches. The first directly uses a known space–time boundary integral equation to determine the problem solution. In the second one, after having defined an artificial boundary delimiting the region of computational interest, the above mentioned integral equation is interpreted as a non reflecting boundary condition to be coupled with a classical finite element method. For such problems, we show that in some cases the computational cost and storage, required by the above numerical approaches, can be significantly reduced by taking into account a property that till now has not been considered. To show the effectiveness of this reduction, the proposed approach is applied to several problems, including multiple scattering.

      PubDate: 2017-10-11T14:37:22Z
  • Spectral viscosity method with generalized Hermite functions for nonlinear
           conservation laws
    • Authors: Xue Luo
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Xue Luo
      In this paper, we propose new spectral viscosity methods based on the generalized Hermite functions for the solution of nonlinear scalar conservation laws in the whole line. It is shown rigorously that these schemes converge to the unique entropy solution by using compensated compactness arguments, under some conditions. The numerical experiments of the inviscid Burger's equation support our result, and it verifies the reasonableness of the conditions.

      PubDate: 2017-10-11T14:37:22Z
  • A plane-wave singularity subtraction technique for the classical Dirichlet
           and Neumann combined field integral equations
    • Authors: Carlos
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Carlos Pérez-Arancibia
      This paper presents expressions for the classical combined field integral equations for the solution of Dirichlet and Neumann exterior Helmholtz problems on the plane, in terms of smooth (continuously differentiable) integrands. These expressions are obtained by means of a singularity subtraction technique based on pointwise plane-wave expansions of the unknown density function. In particular, a novel regularization of the hypersingular operator is obtained, which, unlike regularizations based on Maue's integration-by-parts formula, does not give rise to involved Cauchy principal value integrals. Moreover, the expressions for the combined field integral operators and layer potentials presented in this contribution can be numerically evaluated at target points that are arbitrarily close to the boundary without severely compromising their accuracy. A variety of numerical examples in two spatial dimensions that consider three different Nyström discretizations for smooth domains and domains with corners—one of which is based on direct application of the trapezoidal rule—demonstrates the effectiveness of the proposed higher-order singularity subtraction approach.

      PubDate: 2017-10-03T14:25:01Z
  • A Continuous hp-mesh model for adaptive discontinuous Galerkin schemes
    • Authors: Vít Dolejší; Georg May; Ajay Rangarajan
      Abstract: Publication date: Available online 2 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Vít Dolejší, Georg May, Ajay Rangarajan
      We present a continuous-mesh model for anisotropic hp-adaptation in the context of numerical methods using discontinuous piecewise polynomial approximation spaces. The present work is an extension of a previously proposed mesh-only (h-)adaptation method which uses both a continuous mesh, and a corresponding high-order continuous interpolation operator. In this previous formulation local anisotropy and global mesh density distribution may be determined by analytical optimization techniques, operating on the continuous mesh model. The addition of varying polynomial degree necessitates a departure from purely analytic optimization. However, we show in this article that a global optimization problem may still be formulated and solved by analytic optimization, adding only the necessity to solve numerically a single nonlinear algebraic equation per adaptation step to satisfy a constraint on the total number of degrees of freedom. The result is a tailorsuited continuous mesh with respect to a model for the global interpolation error measured in the L q -norm. From the continuous mesh a discrete triangular mesh may be generated using any metric-based mesh generator.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.015
  • Analysis of Galerkin and streamline-diffusion FEMs on piecewise
           equidistant meshes for turning point problems exhibiting an interior layer
    • Authors: Simon Becher
      Abstract: Publication date: Available online 21 September 2017
      Source:Applied Numerical Mathematics
      Author(s): Simon Becher
      We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise equidistant meshes proposed by Sun and Stynes. We also study the streamline-diffusion finite element method (SDFEM) for such problems. For these methods error estimates uniform with respect to ε are proven in the energy norm and in the stronger SDFEM-norm, respectively. Numerical experiments confirm the theoretical findings.

      PubDate: 2017-09-26T13:37:25Z
  • Convergence and stability analysis of heterogeneous time step coupling
           schemes for parabolic problems
    • Authors: Michal
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Michal Beneš
      We propose and rigorously analyze the subcycling method based on primal domain decomposition techniques for first-order transient partial differential equations. In time dependent problems, it can be computationally advantageous to use different time steps in different regions. Smaller time steps are used in regions of significant changes in the solution and larger time steps are prescribed in regions with nearly stationary response. Subcycling can efficiently reduce the total computational cost. Crucial to our approach is a nonstandard heterogeneous temporal discretization. We begin with the discretization in time by the asynchronous Rothe method, which, in essence, involves a backward finite difference scheme assuming different time steps (fine and large time steps) in different parts of the computational domain. The emphasis of the paper is on qualitative properties of the new numerical scheme, such as a-priori estimates, existence of the time-discrete solutions and the strong convergence and stability analysis. Several numerical experiments were conducted to examine the consistency of the proposed method.

      PubDate: 2017-08-03T13:52:30Z
  • Numerical analysis of an operational Jacobi Tau method for fractional
           weakly singular integro-differential equations
    • Authors: Mokhtary
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): P. Mokhtary
      The main concern of this paper is to develop and analyze an operational Tau method for obtaining the numerical solution of fractional weakly singular integro-differential equations when the Jacobi polynomials are used as natural basis functions. This strategy is an application of the matrix–vector–product approach in Tau formulation of the problem. We first study the regularity of the exact solution and show that some derivatives of the exact solution have a singularity at origin dependence on both order of fractional derivative and weakly singular kernel function which makes poor convergence results for the Tau discretization of the problem. In order to recover high-order of convergence, we propose a new variable transformation to regularize the given functions and then to approximate the solution via a satisfactory order of convergence using an operational Tau method. Convergence analysis of this novel method is presented and the expected spectral rate of convergence for the proposed method is established. Numerical results are given which confirm both the theoretical predictions obtained and efficiency of the proposed method.

      PubDate: 2017-07-12T12:47:24Z
  • Recognition of a time-dependent source in a time-fractional wave equation
    • Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): K. Šišková, M. Slodička
      In the present paper, we deal with an inverse source problem for a time-fractional wave equation in a bounded domain in R d . The time-dependent source is determined from an additional measurement in the form of integral over the space subdomain. The existence, uniqueness and regularity of a weak solution are obtained. A numerical algorithm based on Rothe's method is proposed, a priori estimates are proved and convergence of iterates towards the solution is established.

      PubDate: 2017-07-02T16:25:43Z
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