New algorithm for the numerical solutions of nonlinear third-order differential equations using jacobi-gauss collocation method

Abstract

A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method is easy to implement and yields very accurate results. © 2011 A. H. Bhrawy and W. M. Abd-Elhameed.