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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >A numerical algorithm for the space and time fractional Fokker-Planck equation
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A numerical algorithm for the space and time fractional Fokker-Planck equation

机译：时空分数Fokker-Planck方程的数值算法

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摘要

Purpose - The purpose of this paper is to present an algorithm based on operational Tau method (OTM) for solving fractional Fokker-Planck equation (FFPE) with space- and time-fractional derivatives. Fokker-Planck equation with positive integer order is also considered. Design/methodology/approach - The proposed algorithm converts the desired FFPE to a set of algebraic equations using orthogonal polynomials as basis functions. The paper states some concepts, properties and advantages of proposed algorithm and its applications for solving FFPE. Findings - Some illustrative numerical experiments including linear and nonlinear FFPE are given and some comparisons are made between OTM and variational iteration method, Adomian decomposition method and homotpy perturbation method. Originality/value - Results demonstrate some capabilities of the proposed algorithm such as the simplicity, the accuracy and the convergency. Also, this is the first presentation of this algorithm for FFPE.
机译：目的-本文的目的是提出一种基于操作Tau方法（OTM）的算法，用于求解具有空间和时间分数导数的分数Fokker-Planck方程（FFPE）。还考虑了具有正整数阶的Fokker-Planck方程。设计/方法/方法-提出的算法使用正交多项式作为基函数将所需的FFPE转换为一组代数方程。本文阐述了所提出算法的一些概念，性质和优点及其在解决FFPE中的应用。研究结果-给出了包括线性和非线性FFPE在内的一些示例性数值实验，并对OTM与变分迭代法，Adomian分解法和齐次摄动法进行了一些比较。原创性/价值-结果证明了所提出算法的某些功能，例如简单性，准确性和收敛性。同样，这是该算法针对FFPE的首次展示。

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