Application of modified optimal homotopy perturbation method to higher order boundary value problems in a finite domain

Abstract

This research focuses on the solution of higher order boundary valueproblems by our proposed method Modified Optimal Homotopy Per-turbation Method (MOHPM). A homotopy with an embedding param-eter and Daftardar-Jafari polynomials are used. To control the conver-gence of solution, some auxiliary functions which depend upon variablesand some constants are used. The proposed method is simple, rapid, ef-fective and accurate. The accuracy has been proved by comparing ourresults with the solutions of optimal homotopy perturbation method(OHPM), optimal homotopy asymptotic method (OHAM), variationaliterative method (VIM),variational iteration method using He's poly-nomials (VIMHP), homotopy perturbation method (HPM), Adomandecomposition method (ADM) and Quintic B-Spline Galerkin's scheme.