A High-Order Difference Scheme for the Generalized Cattaneo Equation
Seak-Weng Vong 1*, Hong-Kui Pang 2, Xiao-Qing Jin 11 Department of Mathematics, University of Macau, Macao, P.R. China.
2 School of Mathematical Sciences, Jiangsu Normal University, Xuzhou, P.R. China.
Received 11 March 2012; Accepted (in revised version) 24 April 2012
Available online 27 April 2012
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.
AMS subject classifications: 65M06, 65M12, 65M15, 35Q51
Key words: Fractional Cattaneo equation, $L_1$ approximation, compact finite difference, stability, convergence.
Email: email@example.com (S.-W. Vong), firstname.lastname@example.org (H.-K. Pang), email@example.com (X.-Q. Jin)