Applications of Optimal Homotopy Asymptotic Method (OHAM) to Tenth Order Boundary Value Problem

Abstract

The aim of this paper is to apply the Optimal Homotopy Asymptotic Method (OHAM), a semi-numerical and semi-analytic technique for solving linear and nonlinear Tenth order boundary value problems. The approximate solution of the problem is calculated in terms of a rapidly convergent series. Two bench mark examples have been considered to illustrate the efficiency and implementation of the method and the results are compared with the Variational Iteration Method (VIM). An interesting result of the analysis is that, the OHAM solution is more accurate than the VIM. Moreover, OHAM provides us with a convenient way to control the convergence of approximate solutions. The obtained solutions have shown that OHAM is effective, simpler, easier and explicit.