In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

In this paper, the variational homotopy perturbation method (VHPM) and its convergence is adopted for the Zakharove-Kuznetsov equations (ZK-equations). The aim of this paper is to present an efficient and reliable treatment of the VHPM for the nonlinear partial differential equations and show that this method is convergent. The convergence of the applied method is approved using the method of m...

This paper features a survey of some recent developments in techniques for obtaining approximate analytical solutions of some nonlinear differential equations arising in various fields of science and engineering. Adomian’s decomposition method is applied to some nonlinear problems, and some mathematical tools such as He’s homotopy perturbation method and variational iteration method are introdu...