New analytical approximate solutions of Fifth-order KdV equation

Abstract

In this paper, we have exposed a process of how to implement a new splitting Adomian decomposition homotopy perturbation method to solve fifth-order KdV equations. The new methodology is applied on two kinds of fifth-order KdV equations with initial data: The first is Sawada-Kotera equation and the second its Lax equation. The numerical results we  obtained  from solutions of two kinds of fifth-order KdV equations, have good convergent  and high  accuracy  comparison with other methods in literature. The graphs and tables of the new analytical approximate solutions show the validity, usefulness, and necessity of the process.

Keywords: Splitting scheme, Adomian decomposition, homotopy perturbation method,  fifth-order KdV equation, convergence analysis.

Mathematics Subject Classifications 2010 [MSC]: 76S05, 65N99, 35Q35