A Nonclassical Radau Collocation Method for Nonlinear Initial-Value Problems with Applications to Lane-Emden Type Equations

Abstract

We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value problems to a system of nonlinear algebraic equations. We also present the comparison of this work with some well-known results and show that the present solution is very accurate.