A numerical algorithm for the space and time fractional Fokker‐Planck equation

Abstract

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.

Citation

Karimi Vanani, S. and Aminataei, A. (2012), "A numerical algorithm for the space and time fractional Fokker‐Planck equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 8, pp. 1037-1052. https://doi.org/10.1108/09615531211271853