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

Abstract

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