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

摘要

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