The Effect of Combining the Adomian Decomposition and Homotopy Perturbation Methods on Solving Fifth-Order Boundary Value Problems

Abstract

This paper considers fifth-order boundary value problems with two-point boundary conditions. For the investigation, first, the Adomian decomposition method (ADM) was applied to the equation and then the homotopy perturbation method (HPM) was used to continue the solution. In addition, this combined method was applied to solve two linear and nonlinear experiments. Then the numerical results obtained by other methods were compared. Furthermore, the convergence of the methods was analyzed. In most of the articles, the HPM is used for equations with initial conditions and the ADM is used for equations with initial and boundary conditions. In this study, a combination of two methods (the ADM and HPM) was used to solve equations with boundary conditions. The results of this combined method are remarkable.