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首页> 外文期刊>Journal of Computational Physics >Explicit and implicit finite difference schemes for fractional Cattaneo equation
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Explicit and implicit finite difference schemes for fractional Cattaneo equation

机译：分数阶Cattaneo方程的显式和隐式有限差分格式。

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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.
机译：本文研究了描述异常扩散的分数阶（非整数）阶Cattaneo方程的数值解。已经开发了两个有限差分方案，即显式预测器-校正器和完全隐式方案。在开发每种方案时，已经考虑了用于控制方程的单独公式化方法。显式的预测器校正器方案是众所周知的MacCormack方案的分数广义化，并且被称为Generalized MacCormack方案。该方案解决了两个耦合的低阶方程，并同时使用主变量计算通量项。然而，完全隐式方案求解单个高阶未分解方程。对于广义MacCormack方案，已经通过傅里叶方法研究了稳定性分析。通过数值测试，发现了两种方案的收敛性实验顺序。然后，讨论了每种方案的适用范围和一些数值性质。

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