A Numerical Method for Lane-Emden Equations Using Chebyshev Polynomials and the Collocation Method

摘要

A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of Chebyshev expansions of function. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.