Finite difference approximations for the fractional Fokker-Planck equation

被引：212

作者：

Chen, S. ^{[2
,3
]}

Liu, F. ^{[1
,2
]}

Zhuang, P. ^{[2
]}

Anh, V. ^{[1
]}

机构：

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[3] Quanzhou Normal Univ, Dept Math, Quanzhou 362000, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2009年 / 33卷 / 01期

基金：

澳大利亚研究理事会; 中国国家自然科学基金;

关键词：

Fractional Fokker-Planck equation; Finite difference approximation; Stability; The energy method; ANOMALOUS DIFFUSION; TRANSPORT; RELAXATION; STABILITY; SYSTEMS; MEDIA;

D O I：

10.1016/j.apm.2007.11.005

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The fractional Fokker-Planck equation has been used in many physical transport problems which take place under the influence or an external force field. In this paper we examine some practical numerical methods to solve a class of initial-boundary value problems for the fractional Fokker-Planck equation on a finite domain. The solvability, stability, consistency, and convergence of these methods are discussed. Their stability is proved by the energy method. Two numerical examples are also presented to evaluate these finite difference methods against the exact analytical Solutions. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：256 / 273

页数：18

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