A second-order numerical method for two-dimensional two-sided space fractional convection diffusion equation

被引：58

作者：

Chen, Minghua ^{[1
]}

Deng, Weihua ^{[1
]}

机构：

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

来源：

APPLIED MATHEMATICAL MODELLING | 2014年 / 38卷 / 13期

基金：

中国国家自然科学基金;

关键词：

Space fractional convection diffusion equation; Numerical stability; Crank-Nicolson scheme; Two-dimensional two-sided fractional PDE; Alternating direction implicit method; FINITE-DIFFERENCE APPROXIMATIONS; DISPERSION; DERIVATIVES;

D O I：

10.1016/j.apm.2013.11.043

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this paper, we discuss the practical alternating directions implicit method to solve the two-dimensional two-sided space fractional convection diffusion equation on a finite domain. We theoretically prove and numerically verify that the presented finite difference scheme is unconditionally von Neumann stable and second order convergent in both space and time directions. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3244 / 3259

页数：16

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