A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives

被引：6

作者：

Sayyar, Golsa ^{[1
]}

Hosseini, Seyed Mohammad ^{[1
]}

Mostajeran, Farinaz ^{[1
]}

机构：

[1] Tarbiat Modares Univ, Fac Math Sci, Dept Appl Math, POB 14115-175, Tehran, Iran

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 104卷

关键词：

Caputo derivative; Fractional diffusion equation; Riesz derivative; Fractional kinetic equation; Weighted and shifted Grunwald difference method; BOUNDARY-VALUE-PROBLEMS; FINITE-ELEMENT-METHOD; DIFFERENCE-METHODS; SPECTRAL METHOD;

D O I：

10.1016/j.camwa.2021.11.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a high-order approach for solving one- and two-dimensional time-space fractional diffusion equations (FDEs) with Caputo-Riesz derivatives. To design the scheme, the Caputo temporal derivative is approximated using a high-order method, and the spatial Riesz derivative is discretized by the second-order weighted and shifted Grunwald difference (WSGD) method. It is proved that the scheme is unconditionally stable and convergent with the order of O (tau(alpha)h(2) + tau(4) ), where tau and h are time and space step sizes, respectively. We illustrate the accuracy and effectiveness of the method by providing several numerical examples.

引用

页码：34 / 43

页数：10

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