Green-Haar method for fractional partial differential equations

Abstract

Purpose

The purpose of this study is to obtain the numerical scheme of finding the numerical solutions of arbitrary order partial differential equations subject to the initial and boundary conditions.

Design/methodology/approach

The authors present a novel Green-Haar approach for the family of fractional partial differential equations. The method comprises a combination of Haar wavelet method with the Green function. To handle the nonlinear fractional partial differential equations the authors use Picard technique along with Green-Haar method.

Findings

The results for some numerical examples are documented in tabular and graphical form to elaborate on the efficiency and precision of the suggested method. The obtained results by proposed method are compared with the Haar wavelet method. The method is better than the conventional Haar wavelet method, for the tested problems, in terms of accuracy. Moreover, for the convergence of the proposed technique, inequality is derived in the context of error analysis.

Practical implications

The authors present numerical solutions for nonlinear Burger’s partial differential equations and two-term partial differential equations.

Originality/value

Engineers and applied scientists may use the present method for solving fractional models appearing in applications.

Citation

Ismail, M., Rehman, M.u. and Saeed, U. (2020), "Green-Haar method for fractional partial differential equations", Engineering Computations, Vol. 37 No. 4, pp. 1473-1490. https://doi.org/10.1108/EC-05-2019-0234