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A High-Order Difference Scheme for the Generalized Cattaneo Equation

Published online by Cambridge University Press:  28 May 2015

Seak-Weng Vong*
Affiliation:
Department of Mathematics, University of Macau, Macao, P.R. China
Hong-Kui Pang*
Affiliation:
School of Mathematical Sciences, Jiangsu Normal University, Xuzhou, P.R. China
Xiao-Qing Jin*
Affiliation:
Department of Mathematics, University of Macau, Macao, P.R. China
*
Corresponding author. Email: swvong@umac.mo
Corresponding author. Email: panghongkui@163.com
Corresponding author. Email: xqjin@umac.mo
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Abstract

A high-order finite difference scheme for the fractional Cattaneo equation is investigated. The L1 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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2012

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