Sayd Siavash Hosseini - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
Azim Aminataei - Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: ۱۶۳۱۵-۱۶۱۸, Tehran, Iran
Fatemeh Kiany - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
Mohsen Zahraei - Department of mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
Mahmood Alizadeh - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

In this paper, we convert the fourth-order differential equations with two-point boundary conditions into a differential equation with homogeneous boundary conditions. Because the decomposition methods are closely related to the McLaren series, the McLaren series has a higher accuracy for points close to zero. Then we use Adomian decomposition and homotopy perturbation methods to solve three linear and nonlinear experiments.

Boundary value problems, Homotopy perturbation method, Adomian Decomposition Method, Modification, stability