International Journal of Computer Mathematics, Volume 95, Issue 1 (2018)

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International Journal of Computer Mathematics, Volume 95, Issue 1 (2018)

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Recent Trends in Highly Accurate and Structure-Preserving Numerical Methods for Partial Differential Equations

Preface

Introduction
Recent trends in highly accurate and structure-preserving numerical methods for partial differential equations
Qin Sheng, Yifa Tang, Bruce A. Wade & Yushun Wang
Pages: 1-2
Published online: 04 Aug 2017
CitationforRecent trends in highly accurate and structure-preserving numerical methods for partial differential equations | Full Text | PDF (266 KB)
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Free Access

Original Articles

Article
A modified exponential method that preserves structural properties of the solutions of the Burgers–Huxley equation
J. E. Macías-Díaz
Pages: 3-19
Published online: 19 Sep 2017
AbstractforA modified exponential method that preserves structural properties of the solutions of the Burgers–Huxley equation | Full Text | References | PDF (1.5 MB)
  • 246 Views
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Article
Adaptive weights for mass conservation in a least-squares finite element method
Hsueh-Chen Lee
Pages: 20-35
Published online: 10 Nov 2017
AbstractforAdaptive weights for mass conservation in a least-squares finite element method | Full Text | References | PDF (2.7 MB)
  • 90 Views
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Article
Analysis of a Fourier pseudo-spectral conservative scheme for the Klein–Gordon–Schrödinger equation
Jialing Wang, Yushun Wang & Dong Liang
Pages: 36-60
Published online: 23 Aug 2017
AbstractforAnalysis of a Fourier pseudo-spectral conservative scheme for the Klein–Gordon–Schrödinger equation | Full Text | References | PDF (2 MB)
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Article
A novel energy-preserving scheme for the coupled nonlinear Schrödinger equations
Zhenguo Mu, Haochen Li & Yushun Wang
Pages: 61-81
Published online: 05 Jan 2018
AbstractforA novel energy-preserving scheme for the coupled nonlinear Schrödinger equations | Full Text | References | PDF (2.9 MB)
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Article
High-order IMEX-WENO finite volume approximation for nonlinear age-structured population model
Santosh Kumar & Paramjeet Singh
Pages: 82-97
Published online: 20 Nov 2017
AbstractforHigh-order IMEX-WENO finite volume approximation for nonlinear age-structured population model | Full Text | References | PDF (2.2 MB)
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Article
Quenching phenomenon in a fractional diffusion equation and its numerical simulation
Yufeng Xu
Pages: 98-113
Published online: 29 Jun 2017
AbstractforQuenching phenomenon in a fractional diffusion equation and its numerical simulation | Full Text | References | PDF (3.9 MB)
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Article
Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs
Wenjun Cai, Yajuan Sun, Yushun Wang & Huai Zhang
Pages: 114-143
Published online: 11 Jun 2017
AbstractforLocal discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs | Full Text | References | PDF (3.2 MB)
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Review

Review
Second-order BDF time approximation for Riesz space-fractional diffusion equations
Hong-lin Liao, Pin Lyu & Seakweng Vong
Pages: 144-158
Published online: 30 Aug 2017
AbstractforSecond-order BDF time approximation for Riesz space-fractional diffusion equations | Full Text | References | PDF (1.1 MB)
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Original Articles

Article
On modified TDRKN methods for second-order systems of differential equations
Julius O. Ehigie, Manman Zou, Xilin Hou & Xiong You
Pages: 159-173
Published online: 04 Jul 2017
AbstractforOn modified TDRKN methods for second-order systems of differential equations | Full Text | References | PDF (1.6 MB)
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Article
Temporal dynamics of the march-in-time toward the steady solution of advection–diffusion systems
Lizhen Chen & Gérard Labrosse
Pages: 174-186
Published online: 31 Jul 2017
AbstractforTemporal dynamics of the march-in-time toward the steady solution of advection–diffusion systems | Full Text | References | PDF (1.3 MB)
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Article
An adaptive FEM with ITP approach for steady Schrödinger equation
Yang Kuang & Guanghui Hu
Pages: 187-201
Published online: 24 Aug 2017
AbstractforAn adaptive FEM with ITP approach for steady Schrödinger equation | Full Text | References | PDF (2.4 MB)
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Article
Finite difference method for time–space linear and nonlinear fractional diffusion equations
Sadia Arshad, Weiping Bu, Jianfei Huang, Yifa Tang & Yue Zhao
Pages: 202-217
Published online: 06 Jul 2017
AbstractforFinite difference method for time–space linear and nonlinear fractional diffusion equations | Full Text | References | PDF (2 MB)
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Article
High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes
Y. D. Zhang, Y. M. Zhao, F. L. Wang & Y. F. Tang
Pages: 218-230
Published online: 20 Nov 2017
AbstractforHigh-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes | Full Text | References | PDF (1 MB)
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Article
Multiderivative extended Runge–Kutta–Nyström methods for multi-frequency oscillatory systems
Jingjun Zhao, Yu Li & Yang Xu
Pages: 231-254
Published online: 23 Aug 2017
AbstractforMultiderivative extended Runge–Kutta–Nyström methods for multi-frequency oscillatory systems | Full Text | References | PDF (3.6 MB)
  • 138 Views
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Article
Stability and convergence of difference schemes for multi-dimensional parabolic equations with variable coefficients and mixed derivatives
Cui-cui Ji, Rui Du & Zhi-zhong Sun
Pages: 255-277
Published online: 16 Oct 2017
AbstractforStability and convergence of difference schemes for multi-dimensional parabolic equations with variable coefficients and mixed derivatives | Full Text | References | PDF (1.7 MB)
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