Explicit and implicit finite difference schemes for fractional Cattaneo equation

Authors:
H. R. Ghazizadeh;M. Maerefat;A. Azimi
Affiliations:
Dept. Mech. Eng., Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran;Dept. Mech. Eng., Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran;Dept. Mech. Eng., Shahid Chamran University of Ahvaz, Ahvaz, Iran
Venue:
Journal of Computational Physics
Year:
2010

Citing 9
Cited 1

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Abstract

In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor-corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor-corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed.