Superlinearly convergent algorithms for the two-dimensional space-time Caputo-Riesz fractional diffusion equation

被引：58

作者：

Chen, Minghua ^{[1
]}

Deng, Weihua ^{[1
]}

Wu, Yujiang ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2013年 / 70卷

基金：

中国国家自然科学基金;

关键词：

Space-time Caputo-Riesz fractional; diffusion equation; Numerical stability; Convergence; PARTIAL-DIFFERENTIAL-EQUATIONS; NUMERICAL-METHODS; APPROXIMATIONS; TERM;

D O I：

10.1016/j.apnum.2013.03.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the space-time Caputo-Riesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify that the implicit finite difference scheme is unconditionally stable (the explicit scheme is conditionally stable with the stability condition tau(gamma)/(Delta x)(alpha) + tau(gamma)/(Delta y)(beta) < C) and 2nd order convergent in space direction, and (2 - gamma)th order convergent in time direction, where gamma is an element of (0, 1]. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：22 / 41

页数：20

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