An efficient spectral collocation algorithm for nonlinear Phi-four equations

Abstract

A Jacobi-Gauss-Lobatto collocation method is developed in this work to obtain spectral solutions for different versions of nonlinear time-dependent Phi-four equations subject to nonhomogeneous initial-boundary conditions. The node points are introduced as the roots of the orthogonal Jacobi polynomial with general parameters, α and β. The objective of this paper is thus to investigate the influence of the Jacobi spectral collocation method for solving the nonlinear Phi-four equations. Moreover, the results obtained with the different Jacobi polynomial parameters, α and β are compared to examine the accuracy of most of these parameters. The accuracy and performance of the proposed method are assessed and evaluated through solving three nonlinear problems. Some numerical experiments are presented to show the convergence and the accuracy of the proposed algorithm. © 2013 Bhrawy et al.