Uniformly Stable Explicitly Solvable Finite Difference Method for Fractional Diffusion Equations

被引：8

作者：

Rui, Hongxing ^{[1
]}

Huang, Jian ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2015年 / 5卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Finite difference scheme; fractional diffusion equation; uniformly stable; explicitly solvable method; asymmetric technique; error estimate; NUMERICAL APPROXIMATION; TRANSPORT; STABILITY;

D O I：

10.4208/eajam.030614.051114a

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A finite difference scheme for the one-dimensional space fractional diffusion equation is presented and analysed. The scheme is constructed by modifying the shifted Grunwald approximation to the spatial fractional derivative and using an asymmetric discretisation technique. By calculating the unknowns in differential nodal point sequences at the odd and even time levels, the discrete solution of the scheme can be obtained explicitly. We prove that the scheme is uniformly stable. The error between the discrete solution and the analytical solution in the discrete l(2) norm is optimal in some cases. Numerical results for several examples are consistent with the theoretical analysis.

引用

页码：29 / 47

页数：19