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Group Iterative Methods for The Solution of Two-dimensional Time-Fractional Diffusion Equation

机译：二维时间分数扩散方程解的组迭代方法

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摘要

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number.
机译：关于空间和/或时间分数衍生物的分数局部微分方程（FPDE）可以描述科学和工程中的各种问题。时间分数扩散方程与标准扩散方程之间的差异主要在于时间衍生物。在过去的几年中，已经证明了从旋转有限差分近似的迭代方案在解决标准扩散方程中很好地工作。然而，仍然尚未调查其对时间分数扩散对应的应用。在本文中，我们将对新的显式组迭代方法进行初步研究，求解二维时间分数扩散方程的新型明确组迭代方法。这些方法源自标准和旋转曲柄 - 尼古尔森差异近似公式。进行了几个数值实验以表明在CPU时间和迭代号方面的开发方案的效率。

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