Laguerre polynomial approach for solving Lane–Emden type functional differential equations

In this paper, a numerical method, which is called the Laguerre collocation method, for the approximate solution of Lane–Emden type functional differential equations in terms of Laguerre polynomials are derived. The method is based on the matrix relations of Laguerre polynomials and their derivatives, and reduces the solution of the Lane–Emden type functional differential equation to the solution of a matrix equation corresponding to system of algebraic equations with the unknown Laguerre coefficients. Also, some illustrative examples are included to demonstrate the validity and applicability of the proposed method.