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

被引：61
|
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.
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页码：1 / 22
页数：22
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