New Galerkin operational matrix of derivatives for solving Lane-Emden singular-type equations

Abstract

A new operational matrix of derivatives of certain nonsymmetric generalized Jacobi polynomials is established and employed for the sake of obtaining new algorithms for handling linear and nonlinear Lane-Emden singular-type IVPs. The suggested algorithms are built on utilizing the Galerkin and collocation spectral methods. The principle idea behind these algorithms is based on converting the problems governed by their initial conditions into systems of linear or nonlinear algebraic equations which can be efficiently solved by suitable solvers. The numerical algorithms are supported by a careful investigation of the convergence analysis of the suggested nonsymmetric generalized Jacobi expansion. Some illustrative examples are given for the sake of indicating the high accuracy and efficiency of the two proposed algorithms.