Jacobi Pseudo-Spectral Method JPSM and BPES for Solving Differential Equations

Abstract

In this paper, a shifted Jacobi pseudo-spectral method JPSM is proposed, along with the Boubaker Polynomials Expansion Scheme BPES, for solving a nonlinear Lane–Emden type equation. The Boubaker Polynomials Expansion Scheme BPES main feature, concerning the embedded boundary conditions, have been outlined. The shifted Jacobi-Gauss points are used as collocation nodes. A numerical example has been included to demonstrate the validity and applicability of the two techniques. It has been revealed that both methods are easy to implement and yield very accurate results.