Numerical Solution of Hunter-Saxton Equation by Using Iterative Methods

Abstract

In this paper, a Hunter-Saxton equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM) and homotopy analysis method (HAM). The approximation solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.