The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: Numerical analysis

被引：57
|
作者：
Li, Changpin [1 ]
Wang, Zhen [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2019年 / 140卷
基金：
中国国家自然科学基金;
关键词：
Caputo derivative; Local discontinuous Galerkin method; Finite difference method; Stability; Convergence; REACTION-DIFFUSION EQUATION; HIGH-ORDER APPROXIMATION; SPECTRAL METHOD; ALGORITHM; DERIVATIVES; SCHEME;
D O I：
10.1016/j.apnum.2019.01.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, three kinds of typical Caputo-type partial differential equations are numerically studied via the finite difference methods/the local discontinuous Galerkin finite element methods, including Caputo-type reaction-diffusion equation, Caputo-type reaction-diffusion-wave equation, and Caputo-type cable equation. The derived numerical schemes are unconditionally stable and convergent. The numerical experiments are also displayed which support the theoretical analysis. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：1 / 22
页数：22
相关论文
共 50 条
  • [41] A new smoothness result for Caputo-type fractional ordinary differential equations
    Li, Binjie
    Xie, Xiaoping
    Zhang, Shiquan
    APPLIED MATHEMATICS AND COMPUTATION, 2019, 349 : 408 - 420
  • [42] The Homotopy Analysis Method for Solving Differential Equations With Generalized Caputo-Type Fractional Derivatives
    Fafa, Wafia
    Odibat, Zaid
    Shawagfeh, Nabil
    JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2023, 18 (02):
  • [43] NUMERICAL SOLUTIONS OF NONAUTONOMOUS STOCHASTIC DELAY DIFFERENTIAL EQUATIONS BY DISCONTINUOUS GALERKIN METHODS
    Dai, Xinjie
    Xiao, Aiguo
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2019, 37 (03) : 447 - 464
  • [44] EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTIONS OF CAPUTO-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS
    Sin, Chung-Sik
    Zheng, Liancun
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (03) : 765 - 774
  • [45] Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise
    Kruse, Raphael
    IMA JOURNAL OF NUMERICAL ANALYSIS, 2014, 34 (01) : 217 - 251
  • [46] Discontinuous Deformation Analysis Coupling with Discontinuous Galerkin Finite Element Methods for Contact Simulations
    Sun, Yue
    Feng, Xiangchu
    Xiao, Jun
    Wang, Ying
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2016, 2016
  • [47] On family of the Caputo-type fractional numerical scheme for solving polynomial equations
    Shams, Mudassir
    Kausar, Nasreen
    Agarwal, Praveen
    Jain, Shilpi
    Salman, Mohammed Abdullah
    Shah, Mohd Asif
    APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING, 2023, 31 (01):
  • [48] COUPLING OF DISCONTINUOUS GALERKIN FINITE ELEMENT AND BOUNDARY ELEMENT METHODS
    Of, G.
    Rodin, G. J.
    Steinbach, O.
    Taus, M.
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (03): : A1659 - A1677
  • [49] WELL-POSEDNESS OF GENERAL CAPUTO-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS
    Sin, Chung-Sik
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (03) : 819 - 832
  • [50] WEll-Posedness of General Caputo-Type Fractional Differential Equations
    Chung-Sik Sin
    Fractional Calculus and Applied Analysis, 2018, 21 : 819 - 832
12345