A new algorithm used Chebyshev pseudospectral method to solve nonlinear second-order Lienard differential equations

Abstract

This article presents a numerical method to determine the approximate solutions of the Lienard equations. It is assumed that the second-order nonlinear Linard differential equations of types u''(x) + f[u(x)]u'(x) + g[u(x)] = 0 on the range [-1; 1] with the given boundary values u[-1] and u[+1]. We have to build a new algorithm to nd the approximate solutions to this problem. This algorithm is based on the pseudospectral method used in the Chebyshev differentiation matrix. In this paper, we used the Mathematica version 10.4 to represent the algorithm, the numerical results and graphics. In the numerical results, we made a comparison between the CPMs numerical results and the Mathematica's numerical results. The biggest odds were very small. Therefore, they will be able to be applied to other nonlinear systems such as the Rayleigh equations and the Emden-fowler equations.