An efficient algorithm based on Haar wavelets for numerical simulation of Fokker-Planck equations with constants and variable coefficients

Abstract

Purpose

The purpose of this paper is to discuss the application of the Haar wavelets for solving linear and nonlinear Fokker-Planck equations with appropriate initial and boundary conditions.

Design/methodology/approach

Haar wavelet approach converts the problems into a system of linear algebraic equations and the obtained system is solved by Gauss-elimination method.

Findings

The accuracy of the proposed scheme is demonstrated on three test examples. The numerical solutions prove that the proposed method is reliable and yields compatible results with the exact solutions. The scheme provides better results than the schemes [9, 14].

Originality/value

The developed scheme is a new scheme for Fokker-Planck equations. The scheme based on Haar wavelets is expended for nonlinear partial differential equations with variable coefficients.

Citation

Kumar, M. and Pandit, S. (2015), "An efficient algorithm based on Haar wavelets for numerical simulation of Fokker-Planck equations with constants and variable coefficients", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 1, pp. 41-56. https://doi.org/10.1108/HFF-03-2014-0084