Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion Equations

被引：0

作者：

Han Zhou

WenYi Tian

Weihua Deng

机构：

[1] Lanzhou University,School of Mathematics and Statistics

来源：

Journal of Scientific Computing | 2013年 / 56卷

关键词：

Quasi-compact difference approximation; Riemann-Liouville fractional derivatives; Stability and convergence; Space fractional diffusion equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, a compact difference operator, termed CWSGD, is designed to establish the quasi-compact finite difference schemes for approximating the space fractional diffusion equations in one and two dimensions. The method improves the spatial accuracy order of the weighted and shifted Grünwald difference (WSGD) scheme (Tian et al., arXiv:1201.5949) from 2 to 3. The numerical stability and convergence with respect to the discrete L2 norm are theoretically analyzed. Numerical examples illustrate the effectiveness of the quasi-compact schemes and confirm the theoretical estimations.

引用

页码：45 / 66

页数：21

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