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 value problems 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 variables and some constants are used. The proposed method is simple, rapid, ef- fective and accurate. The accuracy has been proved by comparing our results with the solutions of optimal homotopy perturbation method (OHPM), optimal homotopy asymptotic method (OHAM), variational iterative method (VIM),variational iteration method using He's poly- nomials (VIMHP), homotopy perturbation method (HPM), Adoman decomposition method (ADM) and Quintic B-Spline Galerkin's scheme.