Approximate solution of singular IVPs of Lane-Emden type and error estimation via advanced Adomian decomposition method

摘要

This article aims to present a simple and effective method, named as advanced Adomian decomposition method, to attain the approximate solution of singular initial value problems of Lane-Emden type. Also, convergence analysis and error analysis with an upper bound of the absolute error for the proposed method are discussed. The proposed method is capable to remove the singular behaviour of the problems and provides an approximate solution up to the desired order. To illustrate the reliability and validity of the proposed method with error estimate several examples that arise in applications are considered and the attained outcomes are compared with some existing numerical methods.