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Explicit and implicit finite difference schemes for fractional Cattaneo equation

✍ Scribed by H.R. Ghazizadeh; M. Maerefat; A. Azimi

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 764 KB
Volume: 229
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2010.05.039

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✦ Synopsis

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.

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