A Jacobi rational pseudospectral method for Lane–Emden initial value problems arising in astrophysics on a semi-infinite interval

Abstract

We derive an operational matrix representation for the differentiation of Jacobi rational functions, which is used to create a new Jacobi rational pseudospectral method based on the operational matrix of Jacobi rational functions. This Jacobi rational pseudospectral method is implemented to approximate solutions to Lane–Emden type equations on semi-infinite intervals. The advantages of using the Jacobi rational pseudospectral method over other techniques are discussed. Indeed, through several numerical examples, including the Lane–Emden problems of first and second kind, we evaluate the accuracy and performance of the proposed method. We also compare our method to other approaches in the literature. The results suggest that the Jacobi rational pseudospectral method is a useful tool for studying Lane–Emden initial value problems, as well as related problems which have regular singular points and are nonlinear.