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Volume 2, Issue 2
A High-Order Difference Scheme for the Generalized Cattaneo Equation

Seak-Weng Vong, Hong-Kui Pang & Xiao-Qing Jin

DOI: 10.4208/eajam.110312.240412a

East Asian J. Appl. Math., 2 (2012), pp. 170-184.

Published online: 2018-02

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M06, 65M12, 65M15, 35Q51

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-2-170, author = {Seak-Weng Vong, Hong-Kui Pang and Xiao-Qing Jin}, title = {A High-Order Difference Scheme for the Generalized Cattaneo Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {2}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.110312.240412a}, url = {http://global-sci.org/intro/article_detail/eajam/10914.html} }
TY - JOUR T1 - A High-Order Difference Scheme for the Generalized Cattaneo Equation AU - Seak-Weng Vong, Hong-Kui Pang & Xiao-Qing Jin JO - East Asian Journal on Applied Mathematics VL - 2 SP - 170 EP - 184 PY - 2018 DA - 2018/02 SN - 2 DO - http://doi.org/10.4208/eajam.110312.240412a UR - https://global-sci.org/intro/article_detail/eajam/10914.html KW - Fractional Cattaneo equation, $L_1$ approximation, compact finite difference, stability, convergence. AB -

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.

Seak-Weng Vong, Hong-Kui Pang and Xiao-Qing Jin. (2018). A High-Order Difference Scheme for the Generalized Cattaneo Equation. East Asian Journal on Applied Mathematics. 2 (2). 170-184. doi:10.4208/eajam.110312.240412a
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