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COMPUTER SCIENCE (1148 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: 67)
ACM Computing Surveys     Hybrid Journal   (Followers: 23)
ACM Journal on Computing and Cultural Heritage     Hybrid Journal   (Followers: 8)
ACM Journal on Emerging Technologies in Computing Systems     Hybrid Journal   (Followers: 13)
ACM Transactions on Accessible Computing (TACCESS)     Hybrid Journal   (Followers: 4)
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)
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Acta Automatica Sinica     Full-text available via subscription   (Followers: 3)
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AEU - International Journal of Electronics and Communications     Hybrid Journal   (Followers: 8)
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AIS Transactions on Human-Computer Interaction     Open Access   (Followers: 6)
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American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Computational Mathematics     Open Access   (Followers: 4)
American Journal of Information Systems     Open Access   (Followers: 6)
American Journal of Sensor Technology     Open Access   (Followers: 2)
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  
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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: 1)
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: 31)
Applied Medical Informatics     Open Access   (Followers: 9)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
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Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
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Archive of Numerical Software     Open Access  
Archives and Museum Informatics     Hybrid Journal   (Followers: 121)
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 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  
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Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Automatica     Hybrid Journal   (Followers: 9)
Automation in Construction     Hybrid Journal   (Followers: 6)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 8)
Basin Research     Hybrid Journal   (Followers: 3)
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Briefings in Bioinformatics     Hybrid Journal   (Followers: 45)
British Journal of Educational Technology     Hybrid Journal   (Followers: 123)
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c't Magazin fuer Computertechnik     Full-text available via subscription   (Followers: 1)
CALCOLO     Hybrid Journal  
Calphad     Hybrid Journal  
Canadian Journal of Electrical and Computer Engineering     Full-text available via subscription   (Followers: 13)
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: 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: 14)
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: 11)
Communication Theory     Hybrid Journal   (Followers: 19)
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: 51)
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)
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Computational Biology and Chemistry     Hybrid Journal   (Followers: 12)
Computational Chemistry     Open Access   (Followers: 2)
Computational Cognitive Science     Open Access   (Followers: 1)
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)
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Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
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Computational Molecular Bioscience     Open Access   (Followers: 2)
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computational Particle Mechanics     Hybrid Journal   (Followers: 1)
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Computer     Full-text available via subscription   (Followers: 81)
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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: 22)
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: 17)
Computer Science and Information Technology     Open Access   (Followers: 11)
Computer Science Education     Hybrid Journal   (Followers: 12)
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  [3042 journals]
  • An error estimate for an energy conserving spectral scheme approximating
           the dynamic elastica with free ends
    • Authors: Kazuho Ito
      Pages: 1 - 20
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Kazuho Ito
      An energy conserving spectral scheme is presented for approximating the smooth solution of the dynamic elastica with free ends. The spatial discretization of the elastica is done on the basis of Galerkin spectral methods with a Legendre grid. It is established that the scheme has the unique solution and enjoys a spectral accuracy with respect to the size of the spatial grid. Moreover, some results of a numerical simulation are given to verify that the implemented scheme preserves the discrete energy.

      PubDate: 2017-05-13T08:01:38Z
      DOI: 10.1016/j.apnum.2017.05.001
      Issue No: Vol. 120 (2017)
  • A note on Hermite multiwavelets with polynomial and exponential vanishing
    • Authors: Mariantonia Cotronei; Nada Sissouno
      Pages: 21 - 34
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Mariantonia Cotronei, Nada Sissouno
      The aim of the paper is to present Hermite-type multiwavelets, i.e. wavelets acting on vector data representing function values and consecutive derivatives, which satisfy the vanishing moment property with respect to elements in the space spanned by exponentials and polynomials. Such functions satisfy a two-scale relation which is level-dependent as well as the corresponding multiresolution analysis. An important feature of the associated filters is the possibility of factorizing their symbols in terms of the so-called cancellation operator. This is shown, in particular, in the situation where Hermite multiwavelets are obtained by completing interpolatory level-dependent Hermite subdivision operators, reproducing polynomial and exponential data, to biorthogonal systems. A few constructions of families of multiwavelet filters of this kind are proposed.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.04.009
      Issue No: Vol. 120 (2017)
  • First order system least squares pseudo-spectral method for
           Stokes–Darcy equations
    • Authors: Peyman Hessari; Byeong-Chun Shin
      Pages: 35 - 52
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Peyman Hessari, Byeong-Chun Shin
      The subject of this paper is to investigate the first order system least squares Legendre and Chebyshev pseudo-spectral methods for coupled Stokes–Darcy equations. By introducing strain tensor as a new variable, Stokes–Darcy equations recast into a system of first order differential equations. The least squares functional is defined by summing up the weighted L 2 -norm of residuals of the first order system for coupled Stokes–Darcy equations. To treat Beavers–Joseph–Saffman interface conditions, the weighted L 2 -norm of these conditions are also added to the least squares functional. Continuous and discrete homogeneous functionals are shown to be equivalent to the combination of weighted H ( div ) and H 1 -norm for Stokes–Darcy equations. The spectral convergence for the Legendre and Chebyshev methods are derived. To demonstrate this analysis, numerical experiments are also presented.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.04.010
      Issue No: Vol. 120 (2017)
  • Error analysis of a compact finite difference method for fourth-order
           nonlinear elliptic boundary value problems
    • Authors: Yuan-Ming Wang
      Pages: 53 - 67
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Yuan-Ming Wang
      This paper is concerned with a compact finite difference method with non-isotropic mesh sizes for a two-dimensional fourth-order nonlinear elliptic boundary value problem. By the discrete energy analysis, the optimal error estimates in the discrete L 2 , H 1 and L ∞ norms are obtained without any constraint on the mesh sizes. The error estimates show that the compact finite difference method converges with the convergence rate of fourth-order. Based on a high-order approximation of the solution, a Richardson extrapolation algorithm is developed to make the final computed solution sixth-order accurate. Numerical results demonstrate the high-order accuracy of the compact finite difference method and its extrapolation algorithm in the discrete L 2 , H 1 and L ∞ norms.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.04.011
      Issue No: Vol. 120 (2017)
  • Optimal error estimate of a compact scheme for nonlinear Schrödinger
    • Authors: Jialin Hong; Lihai Ji; Linghua Kong; Tingchun Wang
      Pages: 68 - 81
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Jialin Hong, Lihai Ji, Linghua Kong, Tingchun Wang
      It has been pointed out in literature that the symplectic scheme of a nonlinear Hamiltonian system can not preserve the total energy in the discrete sense Ge and Marsden (1988) [10]. Moreover, due to the difficulty in obtaining a priori estimate of the numerical solution, it is very hard to establish the optimal error bound of the symplectic scheme without any restrictions on the grid ratios. In this paper, we develop and analyze a compact scheme for solving nonlinear Schrödinger equation. We introduce a cut-off technique for proving optimal L ∞ error estimate for the compact scheme. We show that the convergence of the compact scheme is of second order in time and of fourth order in space. Meanwhile, we define a new type of energy functional by using a recursion relationship, and then prove that the compact scheme is mass and energy-conserved, symplectic-conserved, unconditionally stable and can be computed efficiently. Numerical experiments confirm well the theoretical analysis results.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.05.004
      Issue No: Vol. 120 (2017)
  • A smoothing Newton method for absolute value equation associated with
           second-order cone
    • Authors: Xin-He Miao; Jian-Tao Yang; B. Saheya; Jein-Shan Chen
      Pages: 82 - 96
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Xin-He Miao, Jian-Tao Yang, B. Saheya, Jein-Shan Chen
      In this paper, we consider the smoothing Newton method for solving a type of absolute value equations associated with second order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. Based on a class of smoothing functions, we reformulate the SOCAVE as a family of parameterized smooth equations, and propose the smoothing Newton algorithm to solve the problem iteratively. Moreover, the algorithm is proved to be locally quadratically convergent under suitable conditions. Preliminary numerical results demonstrate that the algorithm is effective. In addition, two kinds of numerical comparisons are presented which provides numerical evidence about why the smoothing Newton method is employed and also suggests a suitable smoothing function for future numerical implementations. Finally, we point out that although the main idea for proving the convergence is similar to the one used in the literature, the analysis is indeed more subtle and involves more techniques due to the feature of second-order cone.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.04.012
      Issue No: Vol. 120 (2017)
  • Two-step algorithms for the stationary incompressible Navier–Stokes
           equations with friction boundary conditions
    • Authors: Hailong Qiu; Rong An; Liquan Mei; Changfeng Xue
      Pages: 97 - 114
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Hailong Qiu, Rong An, Liquan Mei, Changfeng Xue
      Two-step algorithms for the stationary incompressible Navier–Stokes equations with friction boundary conditions are considered in this paper. Our algorithms consist of solving one Navier–Stokes variational inequality problem used the linear equal-order finite element pair (i.e., P 1 – P 1 ) and then solving a linearization variational inequality problem used the quadratic equal-order finite element pair (i.e., P 2 – P 2 ). Moreover, the stability and convergence of our two-step algorithms are derived. Finally, numerical tests are presented to check theoretical results.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.05.003
      Issue No: Vol. 120 (2017)
  • Truncated transparent boundary conditions for second order hyperbolic
    • Authors: Ivan Sofronov
      Pages: 115 - 124
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Ivan Sofronov
      In [22] we announced equations for yielding differential operators of transparent boundary conditions (TBCs) for a certain class of second order hyperbolic systems. Here we present the full derivation of these equations and consider ways of their solving. The solutions represent local parts of TBCs, and they can be used as approximate nonreflecting boundary conditions. We give examples of computing such conditions called ‘truncated TBCs’ for 3D elasticity and Biot poroelasticity

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.05.002
      Issue No: Vol. 120 (2017)
  • Second order approximations for kinetic and potential energies in
           Maxwell's wave equations
    • Authors: J.A. Ferreira; D. Jordão; L. Pinto
      Pages: 125 - 140
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): J.A. Ferreira, D. Jordão, L. Pinto
      In this paper we propose a numerical scheme for wave type equations with damping and space variable coefficients. Relevant equations of this kind arise for instance in the context of Maxwell's equations, namely, the electric potential equation and the electric field equation. The main motivation to study such class of equations is the crucial role played by the electric potential or the electric field in enhanced drug delivery applications. Our numerical method is based on piecewise linear finite element approximation and it can be regarded as a finite difference method based on non-uniform partitions of the spatial domain. We show that the proposed method leads to second order convergence, in time and space, for the kinetic and potential energies with respect to a discrete L 2 -norm.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.05.005
      Issue No: Vol. 120 (2017)
  • A mixed finite element approximation for Darcy–Forchheimer flows of
           slightly compressible fluids
    • Authors: Thinh Kieu
      Pages: 141 - 164
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Thinh Kieu
      In this paper, we consider the generalized Forchheimer flows for slightly compressible fluids in porous media. Using Muskat's and Ward's general form of Forchheimer equations, we describe the flow of a single-phase fluid in R d , d ≥ 2 by a nonlinear degenerate system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stability of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. The continuous dependence of numerical solutions on physical parameters are demonstrated. Experimental studies are presented regarding convergence rates and showing the dependence of the solution on the physical parameters.

      PubDate: 2017-06-06T14:38:08Z
      DOI: 10.1016/j.apnum.2017.05.006
      Issue No: Vol. 120 (2017)
  • Single measurement experimental data for an inverse medium problem
           inverted by a multi-frequency globally convergent numerical method
    • Authors: Aleksandr E. Kolesov; Michael V. Klibanov; Loc H. Nguyen; Dinh-Liem Nguyen; Nguyen T. Thành
      Pages: 176 - 196
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Aleksandr E. Kolesov, Michael V. Klibanov, Loc H. Nguyen, Dinh-Liem Nguyen, Nguyen T. Thành
      The recently developed globally convergent numerical method for an inverse medium problem with the data resulting from a single measurement, proposed in [23], is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the frequency domain with the multi-frequency data. Due to a significant amount of noise in the measured data, a straightforward application of the Fourier transform to these data does not work. Hence, we develop a heuristic data preprocessing procedure, which is described in the paper. The preprocessed data are used as the input for the inversion algorithm. Numerical results demonstrate a good accuracy of the reconstruction of both refractive indices and locations of targets.

      PubDate: 2017-06-06T14:38:08Z
      DOI: 10.1016/j.apnum.2017.05.007
      Issue No: Vol. 120 (2017)
  • Stability and error analysis of the reproducing kernel Hilbert space
           method for the solution of weakly singular Volterra integral equation on
           graded mesh
    • Authors: Hossein Beyrami; Taher Lotfi; Katayoun Mahdiani
      Pages: 197 - 214
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Hossein Beyrami, Taher Lotfi, Katayoun Mahdiani
      In this article, we approximate the solution of the weakly singular Volterra integral equation of the second kind using the reproducing kernel Hilbert space (RKHS) method. This method does not require any background mesh and can easily be implemented. Since the solution of the second kind weakly singular Volterra integral equation has unbounded derivative at the left end point of the interval of the integral equation domain, RKHS method has poor convergence rate on the conventional uniform mesh. Consequently, the graded mesh is proposed. Using error analysis, we show the RKHS method has better convergence rate on the graded mesh than the uniform mesh. Numerical examples are given to confirm the error analysis results. Regularization of the solution is an alternative approach to improve the efficiency of the RKHS method. In this regard, an smooth transformation is used to regularization and obtained numerical results are compared with other methods.

      PubDate: 2017-06-12T13:07:08Z
      DOI: 10.1016/j.apnum.2017.05.010
      Issue No: Vol. 120 (2017)
  • Strong convergence of the split-step theta method for neutral stochastic
           delay differential equations
    • Authors: Zhiping Yan; Aiguo Xiao; Xiao Tang
      Pages: 215 - 232
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Zhiping Yan, Aiguo Xiao, Xiao Tang
      Neutral stochastic delay differential equations often appear in various fields of science and engineering. The aim of this article is to investigate the strong convergence of the split-step theta (SST) method for the neutral stochastic delay differential equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In particular, we reveal that the SST method with θ ∈ [ 0 , 1 ] strongly converges to the exact solution with the order 1 2 . Some numerical results are presented to confirm the obtained results.

      PubDate: 2017-06-12T13:07:08Z
      DOI: 10.1016/j.apnum.2017.05.008
      Issue No: Vol. 120 (2017)
  • Exponentially graded mesh for a singularly perturbed problem with two
           small parameters
    • Authors: Helena Zarin
      Pages: 233 - 242
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Helena Zarin
      A one-dimensional singularly perturbed boundary value problem with two small perturbation parameters is numerically solved on an exponentially graded mesh. Using an h-version of the standard Galerkin method with higher order polynomials, we prove a robust convergence in the corresponding energy norm. Numerical experiments support theoretical findings.

      PubDate: 2017-06-21T15:41:03Z
      DOI: 10.1016/j.apnum.2017.06.003
      Issue No: Vol. 120 (2017)
  • Unconditional error estimates for time dependent viscoelastic fluid flow
    • Authors: Haibiao Zheng; Jiaping Yu; Li Shan
      Pages: 1 - 17
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Haibiao Zheng, Jiaping Yu, Li Shan
      The unconditional convergence of finite element method for two-dimensional time-dependent viscoelastic flow with an Oldroyd B constitutive equation is given in this paper, while all previous works require certain time-step restrictions. The approximation is stabilized by using the Discontinuous Galerkin (DG) approximation for the constitutive equation. The analysis bases on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element approximation of corresponding iterated time-discrete PDEs. The approach used in this paper can be applied to more general couple nonlinear parabolic and hyperbolic systems.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.010
      Issue No: Vol. 119 (2017)
  • A numerical method for solving the time variable fractional order
           mobile–immobile advection–dispersion model
    • Authors: Wei Jiang; Na Liu
      Pages: 18 - 32
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Wei Jiang, Na Liu
      In this article, we proposed a new numerical method to obtain the approximation solution for the time variable fractional order mobile–immobile advection–dispersion model based on reproducing kernel theory and collocation method. The equation is obtained from the standard advection–dispersion equation (ADE) by adding the Coimbra's variable fractional derivative in time of order γ ( x , t ) ∈ [ 0 , 1 ] . In order to solve this kind of equation, we discuss and derive the ε-approximate solution in the form of series with easily computable terms in the bivariate spline space. At the same time, the stability and convergence of the approximation are investigated. Finally, numerical examples are provided to show the accuracy and effectiveness.

      PubDate: 2017-04-11T18:11:42Z
      DOI: 10.1016/j.apnum.2017.03.014
      Issue No: Vol. 119 (2017)
  • Difference schemes for systems of second order nonlinear ODEs on a
           semi-infinite interval
    • Authors: M. Król; M.V. Kutniv; O.I. Pazdriy
      Pages: 33 - 50
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): M. Król, M.V. Kutniv, O.I. Pazdriy
      The three-point difference schemes of high order accuracy for the numerical solving boundary value problems on a semi-infinite interval for systems of second order nonlinear ordinary differential equations with a not self-conjugate operator are constructed and justified. We proved the existence and uniqueness of solutions of the three-point difference schemes and obtained the estimate of their accuracy. The results of numerical experiments which confirm the theoretical results are given.

      PubDate: 2017-04-11T18:11:42Z
      DOI: 10.1016/j.apnum.2017.03.012
      Issue No: Vol. 119 (2017)
  • Spectral element technique for nonlinear fractional evolution equation,
           stability and convergence analysis
    • Authors: Mehdi Dehghan; Mostafa Abbaszadeh
      Pages: 51 - 66
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Mehdi Dehghan, Mostafa Abbaszadeh
      In the current manuscript, we consider a fractional partial integro-differential equation that is called fractional evolution equation. The fractional evolution equation is based on the Riemann–Liouville fractional integral. The presented numerical algorithm is based on the following procedures: at first a difference scheme has been used to discrete the temporal direction and secondly the spectral element method is applied to discrete the spatial direction and finally these procedures are combined to obtain a full-discrete scheme. For the constructed numerical technique, we prove the unconditional stability and also obtain an error bound. We use the energy method to analysis the full-discrete scheme. We employ some test problems to show the high accuracy of the proposed technique. Also, we compare the obtained numerical results using the present method with the existing methods in the literature.

      PubDate: 2017-04-19T19:09:14Z
      DOI: 10.1016/j.apnum.2017.03.009
      Issue No: Vol. 119 (2017)
  • Second order time relaxation model for accelerating convergence to
           steady-state equilibrium for Navier–Stokes equations
    • Authors: Osman Rasit Isik; Aziz Takhirov; Haibiao Zheng
      Pages: 67 - 78
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Osman Rasit Isik, Aziz Takhirov, Haibiao Zheng
      This paper deals with the problem of accelerating convergence to equilibrium for the Navier–Stokes equation using time relaxation models. We show that the BDF2 based semidiscrete solution of the regularized scheme converges to the steady-state solution of the continuous Navier–Stokes equations, under appropriate conditions. The proof also shows that time relaxation model can be used to accelerate the convergence with the appropriate choice of the parameters. Numerical experiment is presented to illustrate the theory.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.03.016
      Issue No: Vol. 119 (2017)
  • A new approach to the construction of DIMSIMs of high order and stage
    • Authors: I.Th. Famelis; Z. Jackiewicz
      Pages: 79 - 93
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): I.Th. Famelis, Z. Jackiewicz
      In this work we describe a new approach to the construction of diagonally implicit multistage integration methods (DIMSIMs) for the numerical solution of initial value problems for ordinary differential equations (ODEs). Differential Evolution, a very popular computational intelligence technique is employed to construct type 1 and type 2 methods with better or equivalent characteristics to the methods presented in the literature. The numerical results in selected problems justify this argument.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.03.015
      Issue No: Vol. 119 (2017)
  • Order reduction phenomenon for general linear methods
    • Authors: Michał Braś; Angelamaria Cardone; Zdzisław Jackiewicz; Bruno Welfert
      Pages: 94 - 114
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Michał Braś, Angelamaria Cardone, Zdzisław Jackiewicz, Bruno Welfert
      The order reduction phenomenon for general linear methods (GLMs) for stiff differential equations is investigated. It turns out that, similarly as for standard Runge–Kutta methods, the effective order of convergence for a large class of GLMs applied to stiff differential systems, is equal to the stage order of the method. In particular, it is demonstrated that the global error ‖ e [ n ] ‖ of GLMs of order p and stage order q applied to the Prothero–Robinson test problem y ′ ( t ) = λ ( y ( t ) − φ ( t ) ) + φ ′ ( t ) , t ∈ [ t 0 , T ] , y ( t 0 ) = φ ( t 0 ) , is O ( h q ) + O ( h p ) as h → 0 and h λ → − ∞ . Moreover, for GLMs with Runge–Kutta stability which are A ( 0 ) -stable and for which the stability function R ( z ) of the underlying Runge–Kutta methods, (i.e., the corresponding RK methods which have the same absolute stability properties as the GLMs), is such that R ( ∞ ) ≠ 1 , the global error satisfies ‖ e [ n ] ‖ = O ( h q + 1 ) + O ( h p ) as h → 0 and h λ → − ∞ . These results are confirmed by numerical experiments.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.001
      Issue No: Vol. 119 (2017)
  • A meshless scheme for Hamiltonian partial differential equations with
           conservation properties
    • Authors: Zhengjie Sun; Wenwu Gao
      Pages: 115 - 125
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Zhengjie Sun, Wenwu Gao
      Based on quasi-interpolation, the paper proposes a meshless scheme for Hamiltonian PDEs with conservation properties. There are two key features of the proposed scheme. First, it is constructed from scattered sampling data. Second, it conserves energy for both linear and nonlinear Hamiltonian PDEs. Moreover, if the considered Hamiltonian PDEs additionally possess some other quadric invariants (i.e., the mass in the Schrödinger equation), then it can even preserve them. Error estimates (including the truncation error and the global error) of the scheme are also derived in the paper. To demonstrate the efficiency and superiority of the scheme, some numerical examples are provided at the end of the paper. Both theoretical and numerical results demonstrate that the scheme is simple, easy to compute, efficient and stable. More importantly, the scheme conserves the discrete energy and thus captures the long-time dynamics of Hamiltonian systems.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.005
      Issue No: Vol. 119 (2017)
  • Neumann problems of 2D Laplace's equation by method of fundamental
    • Authors: Zi-Cai Li; Ming-Gong Lee; Hung-Tsai Huang; John Y. Chiang
      Pages: 126 - 145
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Zi-Cai Li, Ming-Gong Lee, Hung-Tsai Huang, John Y. Chiang
      The method of fundamental solutions (MFS) was first used by Kupradze in 1963 [21]. Since then, there have appeared numerous reports of the MFS. Most of the existing analysis for the MFS are confined to Dirichlet problems on disk domains. It seems to exist no analysis for Neumann problems. This paper is devoted to Neumann problems in non-disk domains, and the new stability analysis and the error analysis are made. The bounds for both condition numbers and errors are derived in detail. The optimal convergence rates in L 2 and H 1 norms in S are achieved, and the condition number grows exponentially as the number of fundamental functions increases. To reduce the huge condition numbers, the truncated singular value decomposition (TSVD) may be solicited. Numerical experiments are provided to support the analysis made. The analysis for Neumann problems in this paper is intriguing due to its distinct features.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.004
      Issue No: Vol. 119 (2017)
  • A fast solution technique for finite element discretization of the
           space–time fractional diffusion equation
    • Authors: Zhengguang Liu; Aijie Cheng; Xiaoli Li; Hong Wang
      Pages: 146 - 163
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Zhengguang Liu, Aijie Cheng, Xiaoli Li, Hong Wang
      In this paper, we study fast Galerkin finite element methods to solve a space–time fractional diffusion equation. We develop an optimal piecewise-linear and piecewise-quadratic finite element methods for solving this problem and give optimal error estimates. Furthermore, we develop piecewise-constant discontinuous finite element method for discontinuous problem of this model. Importantly, a fast solution technique to accelerate non-square Toeplitz matrix–vector multiplications which arise from both continuous and discontinuous Galerkin finite element discretization respectively is considered. This fast solution technique is based on fast Fourier transform and depends on the special structure of coefficient matrices and it helps to reduce the computational work from O ( N 3 ) required by the traditional methods to O ( N log 2 ⁡ N ) , where N is the size (number of spatial grid points) of the coefficient matrices for every time step. Moreover, the applicability and accuracy of the method are demonstrated by numerical experiments to support our theoretical analysis.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.003
      Issue No: Vol. 119 (2017)
  • Efficient implementation of RKN-type Fourier collocation methods for
           second-order differential equations
    • Authors: Bin Wang; Fanwei Meng; Yonglei Fang
      Pages: 164 - 178
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Bin Wang, Fanwei Meng, Yonglei Fang
      In this paper we discuss the efficient implementation of RKN-type Fourier collocation methods, which are used when solving second-order differential equations. The proposed implementation relies on an alternative formulation of the methods and their blended formulation. The features and effectiveness of the implementation are confirmed by the performance of the methods on three numerical tests.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.008
      Issue No: Vol. 119 (2017)
  • A second order operator splitting numerical scheme for the
           “good” Boussinesq equation
    • Authors: Cheng Zhang; Hui Wang; Jingfang Huang; Cheng Wang; Xingye Yue
      Pages: 179 - 193
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Cheng Zhang, Hui Wang, Jingfang Huang, Cheng Wang, Xingye Yue
      The nonlinear stability and convergence analyses are presented for a second order operator splitting scheme applied to the “good” Boussinesq equation, coupled with the Fourier pseudo-spectral approximation in space. Due to the wave equation nature of the model, we have to rewrite it as a system of two equations, for the original variable u and v = u t , respectively. In turn, the second order operator splitting method could be efficiently designed. A careful Taylor expansion indicates the second order truncation error of such a splitting approximation, and a linearized stability analysis for the numerical error function yields the desired convergence estimate in the energy norm. In more details, the convergence in the energy norm leads to an ℓ ∞ ( 0 , T ⁎ ; H 2 ) convergence for the numerical solution u and ℓ ∞ ( 0 , T ⁎ ; ℓ 2 ) convergence for v = u t . And also, the presented convergence is unconditional for the time step in terms of the spatial grid size, in comparison with a severe time step restriction, Δ t ≤ C h 2 , required in many existing works.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.006
      Issue No: Vol. 119 (2017)
  • Numerical analysis of cubic orthogonal spline collocation methods for the
           coupled Schrödinger–Boussinesq equations
    • Authors: Feng Liao; Luming Zhang; Shanshan Wang
      Pages: 194 - 212
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Feng Liao, Luming Zhang, Shanshan Wang
      In this article, we formulate two orthogonal spline collocation schemes, which consist of a nonlinear and a linear scheme for solving the coupled Schrödinger–Boussinesq equations numerically. Firstly, the conservation laws of our schemes are derived. Secondly, the existence solutions of our schemes are investigated. Thirdly, the convergence and stability of the nonlinear scheme are analyzed by means of discrete energy methods, while the convergence of the linear scheme is proved by cut-off function technique. Finally, numerical results are reported to verify our theoretical analysis for the numerical methods.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.007
      Issue No: Vol. 119 (2017)
  • A second-order hybrid finite volume method for solving the Stokes equation
    • Authors: Zhongying Chen; Yuesheng Xu; Jiehua Zhang
      Pages: 213 - 224
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Zhongying Chen, Yuesheng Xu, Jiehua Zhang
      This paper presents a second-order hybrid finite volume method for solving the Stokes equation on a two dimensional domain. The trial function space of the method for velocity is chosen to be a quadratic conforming finite element space with a hierarchical decomposition technique on triangular meshes, and its corresponding test function space consists of piecewise constant functions and piecewise quadratic polynomial functions based on a dual partition of the domain. The trial function space and test function space of the method for pressure are chosen to be a linear finite element space. We derive the inf-sup conditions of the discrete systems of the method on triangular meshes by using a relationship between the finite volume method and the finite element method. The well-posedness of the proposed finite volume method is obtained by using the Babuska–Lax–Milgram theorem. The error estimates of the optimal order are obtained in the H 1 -norm for velocity and in the L 2 -norm for pressure. Numerical experiments are presented to illustrate the theoretical results.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.002
      Issue No: Vol. 119 (2017)
  • Temporal localized nonlinear model reduction with a priori error estimate
    • Authors: Saifon Chaturantabut
      Pages: 225 - 238
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Saifon Chaturantabut
      This work presents a model reduction framework using a temporal localized basis approach to efficiently reduce the simulation time for nonlinear dynamical systems with rapid changes over a short time period, and proposes a corresponding a priori error bound. This framework employs the proper orthogonal decomposition (POD) to construct localized basis sets from different temporal subdomains, which can be used in the Galerkin projection to accurately capture the important local dynamics of the system. The discrete empirical interpolation method (DEIM) with the corresponding temporal localized basis sets is then applied to efficiently compute the projected nonlinear terms. A heuristic procedure for subdividing snapshots over the temporal domain is proposed. This procedure first partitions the set of snapshots where there are possible significant changes in system dynamics, and then uses the notion of distance between subspaces to later remove unnecessary partitioning. An a priori error bound is derived to confirm the convergence of this framework and to explain how the propagated errors from the localized reduced systems affect the overall accuracy. Numerical experiments demonstrate the accuracy improvement of the temporal localized framework through a parametrized nonlinear miscible flow simulation. The results show the applicability of the proposed approach to various parameter values that are not necessary used for generating the POD and DEIM localized basis sets.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.02.014
      Issue No: Vol. 119 (2017)
  • Construction and implementation of two-step continuous methods for
           Volterra integral equations
    • Authors: Giovanni Capobianco; Dajana Conte; Beatrice Paternoster
      Pages: 239 - 247
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Giovanni Capobianco, Dajana Conte, Beatrice Paternoster
      It is the purpose of this paper to construct an error estimation for highly stable two-step continuous methods derived in [7], in order to use it in a variable stepsize implementation. New families of two step almost collocation methods are constructed, by using a collocation technique which permits to increase the uniform order of one step collocation methods, without increasing the computational cost and by maintaining good stability properties, thus avoiding the order reduction phenomenon. Numerical experiments confirm the effectiveness of the proposed methods.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.02.008
      Issue No: Vol. 119 (2017)
  • Highly symmetric 3-refinement Bi-frames for surface multiresolution
    • Authors: Qingtang Jiang; Dale K. Pounds
      Pages: 1 - 18
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Qingtang Jiang, Dale K. Pounds
      Multiresolution techniques for (mesh-based) surface processing have been developed and successfully used in surface progressive transmission, compression and other applications. A triangular mesh allows 3 , dyadic and 7 refinements. The 3 -refinement is the most appealing one for multiresolution data processing since it has the slowest progression through scale and provides more resolution levels within a limited capacity. The 3 refinement has been used for surface subdivision and for discrete global grid systems. Recently lifting scheme-based biorthogonal bivariate wavelets with high symmetry have been constructed for surface multiresolution processing. If biorthogonal wavelets (with either dyadic or 3 refinement) have certain smoothness, they will have big supports. In other words, the corresponding multiscale algorithms have large templates; and this is undesirable for surface processing. On the other hand, frames provide a flexibility for the construction of system generators (called framelets) with high symmetry and smaller supports. In this paper we study highly symmetric 3 -refinement wavelet bi-frames for surface processing. We design the frame algorithms based on the vanishing moments and smoothness of the framelets. The frame algorithms obtained in this paper are given by templates so that one can easily implement them. We also present interpolatory 3 subdivision-based frame algorithms. In addition, we provide frame ternary multiresolution algorithms for boundary vertices on an open surface.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.02.005
      Issue No: Vol. 118 (2017)
  • Numerical study of an adaptive domain decomposition algorithm based on
           Chebyshev tau method for solving singular perturbed problems
    • Authors: Wenting Shao; Xionghua Wu; Cheng Wang
      Pages: 19 - 32
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Wenting Shao, Xionghua Wu, Cheng Wang
      It is known that spectral methods offer exponential convergence for infinitely smooth solutions. However, they are not applicable for problems presenting singularities or thin layers, especially true for the ones with the location of singularity unknown. An adaptive domain decomposition method (DDM) integrated with Chebyshev tau method based on the highest derivative (CTMHD) is introduced to solve singular perturbed boundary value problems (SPBVPs). The proposed adaptive algorithm uses the refinement indicators based on Chebyshev coefficients to determine which subintervals need to be refined. Numerical experiments have been conducted to demonstrate the superior performance of the method for SPBVPs with a number of singularities including boundary layers, interior layers and dense oscillations. A fourth order nonlinear SPBVP is also concerned. The numerical results illustrate the efficiency and applicability of our adaptive algorithm to capture the locations of singularities, and the higher accuracy in comparison with some existing numerical methods in the literature.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.02.006
      Issue No: Vol. 118 (2017)
  • Spectral discretization of the Navier–Stokes problem with mixed
           boundary conditions
    • Authors: Yasmina Daikh; Driss Yakoubi
      Pages: 33 - 49
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Yasmina Daikh, Driss Yakoubi
      We consider a variational formulation of the three dimensional Navier–Stokes equations provided with mixed boundary conditions. We write this formulation with three independent unknowns: the vorticity, the velocity and the pressure. Next, we propose a discretization by spectral methods. A detailed numerical analysis leads to a priori error estimates for the three unknowns.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.02.002
      Issue No: Vol. 118 (2017)
  • Weak stochastic Runge–Kutta Munthe-Kaas methods for finite spin
    • Authors: M. Ableidinger; E. Buckwar
      Pages: 50 - 63
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): M. Ableidinger, E. Buckwar
      In this article we construct weak Runge–Kutta Munthe-Kaas methods for a finite-dimensional version of the stochastic Landau–Lifshitz equation (LL-equation). We formulate a Lie group framework for the stochastic LL-equation and derive regularity conditions for the corresponding SDE system on the Lie algebra. Using this formulation we define weak Munthe-Kaas methods based on weak stochastic Runge–Kutta methods (SRK methods) and provide sufficient conditions such that the Munthe-Kaas methods inherit the convergence order of the underlying SRK method. The constructed methods are fully explicit and preserve the norm constraint of the LL-equation exactly. Numerical simulations are provided to illustrate the convergence order as well as the long time behaviour of the proposed methods.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.01.017
      Issue No: Vol. 118 (2017)
  • Analysis of order reduction when integrating linear initial boundary value
           problems with Lawson methods
    • Authors: I. Alonso-Mallo; B. Cano; N. Reguera
      Pages: 64 - 74
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): I. Alonso-Mallo, B. Cano, N. Reguera
      In this paper, a thorough analysis is given for the order which is observed when integrating evolutionary linear partial differential equations with Lawson methods. The analysis is performed under the general framework of C0-semigroups in Banach spaces and hence it can be applied to the numerical time integration of many initial boundary value problems which are described by linear partial differential equations. Conditions of regularity and annihilation at the boundary of these problems are then stated to justify the precise order which is observed, including fractional order of convergence.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.02.010
      Issue No: Vol. 118 (2017)
  • An efficient two-level finite element algorithm for the natural convection
    • Authors: Pengzhan Huang
      Pages: 75 - 86
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Pengzhan Huang
      An efficient two-level finite element algorithm for solving the natural convection equations is developed and studied in this paper. By solving one small nonlinear system on a coarse mesh H and two large linearized problems on a fine mesh h = O ( H 7 − ε 2 ) with different loads, we can obtain an approximation solution ( u h , p h , T h ) with the convergence rate of same order as the usual finite element solution, which involves one large nonlinear natural convection system on the same fine mesh h. Furthermore, compared with the results of Si's algorithm in 2011, the given algorithm costs less computed time to get almost the same precision.

      PubDate: 2017-03-09T19:12:42Z
      DOI: 10.1016/j.apnum.2017.02.012
      Issue No: Vol. 118 (2017)
  • High-order numerical solution of the Helmholtz equation for domains with
           reentrant corners
    • Authors: S. Magura; S. Petropavlovsky; S. Tsynkov; E. Turkel
      Pages: 87 - 116
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): S. Magura, S. Petropavlovsky, S. Tsynkov, E. Turkel
      Standard numerical methods often fail to solve the Helmholtz equation accurately near reentrant corners, since the solution may become singular. The singularity has an inhomogeneous contribution from the boundary data near the corner and a homogeneous contribution that is determined by boundary conditions far from the corner. We present a regularization algorithm that uses a combination of analytical and numerical tools to distinguish between these two contributions and ultimately subtract the singularity. We then employ the method of difference potentials to numerically solve the regularized problem with high-order accuracy over a domain with a curvilinear boundary. Our numerical experiments show that the regularization successfully restores the design rate of convergence.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.02.013
      Issue No: Vol. 118 (2017)
  • Galerkin finite element method for the nonlinear fractional
           Ginzburg–Landau equation
    • Authors: Meng Li; Chengming Huang; Nan Wang
      Pages: 131 - 149
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Meng Li, Chengming Huang, Nan Wang
      In this paper, we are concerned with the numerical solution of the nonlinear fractional Ginzburg–Landau equation. Galerkin finite element method is used for the spatial discretization, and an implicit midpoint difference method is employed for the temporal discretization. The boundedness, existence and uniqueness of the numerical solution, and the unconditional error estimates in the L 2 -norm are investigated in details. To numerically solve the nonlinear system, linearized iterative algorithms are also considered. Finally, some numerical examples are presented to illustrate the effectiveness of the algorithm.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.03.003
      Issue No: Vol. 118 (2017)
  • Design and evaluation of homotopies for efficient and robust continuation
    • Authors: David A. Brown; David W. Zingg
      Pages: 150 - 181
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): David A. Brown, David W. Zingg
      Homotopy continuation, in combination with a quasi-Newton method, can be an efficient and robust technique for solving large sparse systems of nonlinear equations. The homotopy itself is pivotal in determining the efficiency and robustness of the continuation algorithm. As the homotopy is defined implicitly by a nonlinear system of equations to which the analytical solution is by assumption unknown, many properties of the homotopy can only be studied using numerical methods. The properties of a given homotopy which have the greatest impact on the corresponding continuation algorithm are traceability and linear solver performance. Metrics are presented for the analysis and characterization of these properties. Several homotopies are presented and studied using these metrics in the context of a parallel implicit three-dimensional Newton–Krylov–Schur flow solver for computational fluid dynamics. Several geometries, grids, and flow types are investigated in the study. Additional studies include the impact of grid refinement and the application of a coordinate transformation to the homotopy as measured through the traceability and linear solver performance metrics.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.03.001
      Issue No: Vol. 118 (2017)
  • Analysis of output-based error estimation for finite element methods
    • Authors: Hugh A. Carson; David L. Darmofal; Marshall C. Galbraith; Steven R. Allmaras
      Pages: 182 - 202
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Hugh A. Carson, David L. Darmofal, Marshall C. Galbraith, Steven R. Allmaras
      In this paper, we develop a priori estimates for the convergence of outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Output error estimates for order p finite element solutions are constructed using the Dual-Weighted Residual (DWR) method with a higher-order p ′ > p dual solution. Specifically, we analyze these DWR estimates for Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods applied to the Poisson problem. For all discretizations, as h → 0 , we prove that the output and output error estimate converge at order 2p and 2 p ′ (assuming sufficient smoothness), while localizations of the output and output error estimate converge at 2 p + d and p + p ′ + d . For DG, the results use a new post processing for the error associated with the lifting operator. For HDG, these rates improve an additional order when the stabilization is based upon an O ( 1 ) length scale.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.004
      Issue No: Vol. 118 (2017)
  • On fractional backward differential formulas for fractional delay
           differential equations with periodic and anti-periodic conditions
    • Authors: M. Saedshoar Heris; M. Javidi
      Pages: 203 - 220
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): M. Saedshoar Heris, M. Javidi
      In this paper, fractional backward differential formulas (FBDF) are presented for the numerical solution of fractional delay differential equations (FDDEs) of the form λ n 0 C D t α n y ( t ) + λ n − 1 0 C D t α n − 1 y ( t ) + ⋯ + λ 1 0 C D t α 1 y ( t ) + λ n + 1 y ( t − τ ) = f ( t ) , t ∈ [ 0 , T ] , where λ i ∈ R ( i = 1 , ⋯ , n + 1 ) , λ n + 1 ≠ 0 , 0 ⩽ α 1 < α 2 < ⋯ < α n < 1 , T > 0 , in Caputo sense. Our investigation is focused on stability properties of the numerical methods and we determine stability regions for the FDDEs. Also we find the Green's functions for this equation corresponding to periodic/anti-periodic conditions in terms of the functions of Mittag Leffler type. Numerical tests are presented to confirm the strength of the approach under investigation.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.03.006
      Issue No: Vol. 118 (2017)
  • IMEX peer methods for fast-wave–slow-wave problems
    • Authors: Behnam Soleimani; Oswald Knoth; Rüdiger Weiner
      Pages: 221 - 237
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Behnam Soleimani, Oswald Knoth, Rüdiger Weiner
      Differential equations with both stiff and nonstiff parts can be solved efficiently by implicit–explicit (IMEX) methods. There have been considered various approaches in the literature. In this paper we introduce IMEX peer methods. We show that the combination of s-stage explicit and implicit peer methods, both of order p, gives an IMEX peer method of the same order. We construct methods of order p = s for s = 3 , 4 , where we compute the free parameters numerically to give good stability with respect to fast-wave–slow-wave problems from weather prediction. We implement these methods with and without step size control. Tests and comparisons with other methods for problems mostly from weather prediction show the high potential of IMEX peer methods.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.02.016
      Issue No: Vol. 118 (2017)
  • Analysis of a group finite element formulation
    • Authors: Gabriel R. Barrenechea; Petr Knobloch
      Pages: 238 - 248
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Gabriel R. Barrenechea, Petr Knobloch
      The group finite element formulation is a strategy aimed at speeding the assembly of finite element matrices for time-dependent problems. This process modifies the Galerkin matrix of the problem in a non-consistent way. This may cause a deterioration of both the stability and convergence of the method. In this paper we prove results for a group finite element formulation of a convection–diffusion–reaction equation showing that the stability of the original discrete problem remains unchanged under appropriate conditions on the data of the problem and on the discretization parameters. A violation of these conditions may lead to non-existence of solutions, as one of our main results shows. An analysis of the consistency error introduced by the group finite element formulation and its skew-symmetric variant is given.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.008
      Issue No: Vol. 118 (2017)
  • Analysis of non-negativity and convergence of solution of the balanced
           implicit method for the delay Cox–Ingersoll–Ross model
    • Authors: A.S. Fatemion Aghda; Seyed Mohammad Hosseini; Mahdieh Tahmasebi
      Pages: 249 - 265
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): A.S. Fatemion Aghda, Seyed Mohammad Hosseini, Mahdieh Tahmasebi
      The delay Cox–Ingersoll–Ross (CIR) model is an important model in the financial markets. It has been proved that the solution of this model is non-negative and its pth moments are bounded. However, there is no explicit solution for this model. So, proposing appropriate numerical method for solving this model which preserves non-negativity and boundedness of the model's solution is very important. In this paper, we concentrate on the balanced implicit method (BIM) for this model and show that with choosing suitable control functions the BIM provides numerical solution that preserves non-negativity of solution of the model. Moreover, we show the pth moment boundedness of the numerical solution of the method and prove the convergence of the proposed numerical method. Finally, we present some numerical examples to confirm the theoretical results, and also application of BIM to compute some financial quantities.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.007
      Issue No: Vol. 118 (2017)
  • BDF-type shifted Chebyshev approximation scheme for fractional functional
           differential equations with delay and its error analysis
    • Authors: V.G. Pimenov; A.S. Hendy
      Pages: 266 - 276
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): V.G. Pimenov, A.S. Hendy
      A numerical method for fractional order differential equations (FDEs) and constant or time-varying delayed fractional differential equations (FDDEs) is constructed. This method is of BDF-type which is based on the interval approximation of the true solution by truncated shifted Chebyshev series. This approach can be reformulated in an equivalent way as a Runge–Kutta method and its Butcher tableau is given. A detailed local and global truncating errors analysis is deduced for the numerical solutions of FDEs and FDDEs. Illustrative examples are included to demonstrate the validity and applicability of the proposed approach.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.013
      Issue No: Vol. 118 (2017)
  • Quadrature rules and asymptotic expansions for two classes of oscillatory
           Bessel integrals with singularities of algebraic or logarithmic type
    • Authors: Hongchao Kang; Junjie Ma
      Pages: 277 - 291
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Hongchao Kang, Junjie Ma
      In this paper we mainly focus on the quadrature rules and asymptotic expansions for two classes of highly oscillatory Bessel integrals with algebraic or logarithmic singularities. Firstly, by two transformations, we transfer them into the standard types on [ − 1 , 1 ] , and derive two useful asymptotic expansions in inverse powers of the frequency ω. Then, based on the two asymptotic expansions, two methods are presented, respectively. One is the so-called Filon-type method. The other is the more efficient Clenshaw-Curtis–Filon-type method, which can be implemented in O ( N log ⁡ N ) operations, based on Fast Fourier Transform (FFT) and fast computation of the modified moments. Here, through large amount of calculation and analysis, we can construct two important recurrence relations for computing the modified moments accurately, based on the Bessel's equation and some properties of the Chebyshev polynomials. In particular, we also provide error analysis for these methods in inverse powers of the frequency ω. Furthermore, we prove directly from the presented error bounds that these methods share the advantageous property, that the larger the values of the frequency ω, the higher the accuracy. The efficiency and accuracy of the proposed methods are illustrated by numerical examples.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.011
      Issue No: Vol. 118 (2017)
  • A numerical method for the solution of exterior Neumann problems for the
           Laplace equation in domains with corners
    • Authors: Laurita
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): C. Laurita
      In this paper we propose a new boundary integral method for the numerical solution of Neumann problems for the Laplace equation, posed in exterior planar domains with piecewise smooth boundaries. Using the single layer representation of the potential, the differential problem is reformulated as a classical boundary integral equation. The use of a smoothing transformation and the introduction of a modified Gauss–Legendre quadrature formula for the approximation of the singular integrals, which turns out to be convergent, leads us to apply a Nyström type method for the numerical solution of the integral equation. We solve some test problems and present the numerical results in order to show the efficiency of the proposed procedure.

      PubDate: 2017-06-02T14:30:28Z
  • Optimized interface conditions in domain decomposition methods to solve
           reaction-diffusion problems with strong heterogeneity in the coefficients
           in a sectorial domain
    • Authors: Chokri Chniti
      Abstract: Publication date: Available online 7 March 2017
      Source:Applied Numerical Mathematics
      Author(s): Chokri Chniti
      The aim of this paper is to derive an appropriate second order transmission boundary conditions near the corner used in domain decomposition methods to study the reaction-diffusion problems (“ − ∇ . ( ν ( x ) ∇ . ) + η ( x ) . ”) with strong heterogeneity in the coefficients in a singular non-convex domain with Neumann and Dirichlet boundary condition. These transmission condition will be tested and compared numerically with other approaches.

      PubDate: 2017-03-09T19:12:42Z
      DOI: 10.1016/j.apnum.2017.02.015
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