A High-Order Difference Scheme for the Generalized Cattaneo Equation

被引：28

作者：

Vong, Seak-Weng ^{[1
]}

Pang, Hong-Kui ^{[2
]}

Jin, Xiao-Qing ^{[1
]}

机构：

[1] Univ Macau, Dept Math, Taipa, Peoples R China

[2] Jiangsu Normal Univ, Sch Math Sci, Xuzhou, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2012年 / 2卷 / 02期

关键词：

Fractional Cattaneo equation; L-1; approximation; compact finite difference; stability; convergence; VOLTERRA INTEGRODIFFERENTIAL EQUATIONS; FRACTIONAL DIFFUSION EQUATION; TRANSPORT; APPROXIMATIONS; STABILITY;

D O I：

10.4208/eajam.110312.240412a

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A high-order finite difference scheme for the fractional Cattaneo equation is investigated. The L-1 approximation is invoked for the time fractional part, and a compact difference scheme is applied to approximate the second-order space derivative. The stability and convergence rate are discussed in the maximum norm by the energy method. Numerical examples are provided to verify the effectiveness and accuracy of the proposed difference scheme.

引用

页码：170 / 184

页数：15

共 28 条

[1]

[Anonymous], 2006, THEORY APPL FRACTION

[2]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[3] The generalized Cattaneo equation for the description of anomalous transport processes [J].