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A High-Order Difference Scheme for the Generalized Cattaneo Equation

A High-Order Difference Scheme for the Generalized Cattaneo Equation
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Year:    2012

East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 2 : pp. 170–184

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.110312.240412a

East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 2 : pp. 170–184

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Fractional Cattaneo equation $L_1$ approximation compact finite difference stability convergence.

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