A new algorithm used the Chebyshev pseudospectral method to solve the 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 on the range [-1, 1] with the given boundary values. We have to build a new algorithm to find approximate solutions to this problem. This algorithm based on the pseudospectral method using the Chebyshev differentiation matrix (CPM). In this paper, we used the Mathematica version 10.4 to represent the algorithm, 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 Emden-fowler equations.

Numerical modeling of stationary pseudospin waves on a graphene monoatomic films

“…We also find it interesting to further consider the interaction of breathers with each other and with other physical fields, as well as the dynamics of spinons on graphene (fullerene, nanotube) nonplanar surfaces of various topologies. This work is devoted to a numerical study of the model 4 [15], [16]. Within the framework of the proposed model, the problems of approximate calculation of potential fields, approximate solution of the Schrödinger equations and simulation of control of the external field of population levels [8] are solved.…”