A review of the semi-analytic/numerical methods for higher order nonlinear partial equations

Abstract

In this review work we consider how Adomian's decomposition method, Homotopy analysis method and variational iteration method can be used to investigate propagating traveling solitary wave solutions of a seventh order generalized Korteweg and de Vries equation. We compare three methods to see the advantage of the approximate terms of the form of series solutions. These illustrations have shown that these techniques are constructing a fast convergence of the approximate solutions. We have also get experience that this rapid convergence very much depends on type and properties of the solutions of the problems just as in a closed form solutions.