کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
521070 | 867751 | 2010 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Explicit and implicit finite difference schemes for fractional Cattaneo equation Explicit and implicit finite difference schemes for fractional Cattaneo equation](/preview/png/521070.png)
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.
Journal: Journal of Computational Physics - Volume 229, Issue 19, 20 September 2010, Pages 7042–7057