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Numerical solution of fractional Bratu–type BVPs: a generalized variational iteration approach

Reem Assadi (Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates)
Suheil Khuri (Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates)
Issam Louhichi (Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 20 May 2020

Issue publication date: 12 January 2021

133

Abstract

Purpose

The purpose of this study is to implement a newly introduced numerical scheme for the numerical solution of a class of nonlinear fractional Bratu-type boundary value problems (BVPs).

Design/methodology/approach

This strategy is based on a generalization of the variational iteration method (VIM). This proposed generalized VIM (GVIM) is particularly suitable for tackling BVPs.

Findings

This scheme yields accurate solutions for a class of nonlinear fractional Bratu-type BVPs, for which the errors are uniformly distributed across a given domain. A proof of convergence is included. The numerical results confirm that this approach overcomes the deficiency of the VIM and other methods that exist in the literature in the sense that the solution does not deteriorate as the authors move away from the initial starting point.

Originality/value

The method introduced is based on original research that produces new knowledge. To the best of the authors’ knowledge, this is the first time that this GVIM is applied to fractional BVPs.

Keywords

Citation

Assadi, R., Khuri, S. and Louhichi, I. (2021), "Numerical solution of fractional Bratu–type BVPs: a generalized variational iteration approach", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 1, pp. 293-307. https://doi.org/10.1108/HFF-03-2020-0167

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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