The analytical solution and numerical solutions for a two-dimensional multi-term time fractional diffusion and diffusion-wave equation

被引：48

作者：

Shen, Shujun ^{[1
]}

Liu, Fawang ^{[2
]}

Anh, Vo V. ^{[2
]}

机构：

[1] Huaqiao Univ, Sch Math Sci, Quanzhou, Fujian, Peoples R China

[2] Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 345卷

基金：

中国国家自然科学基金; 澳大利亚研究理事会;

关键词：

Multi-term time-fractional diffusion equation; Numerical method; Stability; Convergence; Method of separation of variables; Energy method; PARTIAL-DIFFERENTIAL-EQUATIONS; FOKKER-PLANCK EQUATION; ANOMALOUS DIFFUSION; APPROXIMATION;

D O I：

10.1016/j.cam.2018.05.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the analytical and numerical solutions for a two-dimensional multi-term time-fractional diffusion and diffusion-wave equation. We derive the analytical solution for the equation using the method of separation of variables and properties of the multivariate Mittag-Leffler function. An implicit difference approximation is constructed. Stability and convergence analysis of the numerical scheme are proved by the energy method. Numerical examples are constructed to evaluate the working of the numerical scheme as compared to theoretical analysis. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：515 / 534

页数：20

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