Solving a nonlinear inverse problem of the Camassa-Holm equation

Abstract

In order to solve the nonlinear inverse Camassa-Holm equations, a numerical method is developed by applying finite difference formula to time discrimination and collocation of polynomial scaling functions for spatial variable. Using operational matrix of derivative, the problem is reduced to a set of algebraic equation. An estimation of error bound is investigated for presented method. Also, to show the accuracy of the proposed method, it is applied on two test problems. One of the most important advantages of this work, compared to previous works, is the implementation simplicity.