Numerical solution of Boundary Value Problems by Piecewise Analysis Method

Abstract

In this paper, we use an efficient numerical algorithm for solving two point fourth-order linear  and nonlinear boundary value problems, which is based on the homotopy analysis method (HAM), namely, the piecewise – homotopy analysis method ( P-HAM).The method contains an auxiliary parameter that provides a powerful tool to analysis strongly linear and nonlinear ( without linearization ) problems directly. Numerical examples are presented to compare the results obtained with some existing results found in literatures. Results obtained by the RHAM performed better in terms of accuracy achieved.

Keywords:            Piecewise-homotopy analysis, perturbation, Adomain decomposition method, Variational Iteration, Boundary Value Problems.