The particular motivation of this work is to develop a computational method to calculate exact and analytic approximate solutions to singular strongly nonlinear initial or boundary value problems of Lane-Emden-Fowler type which model many phenomena in mathematical physics and astrophysics. A powerful algorithm is proposed based on the series representation of the solution via suitable base functions. The utilization of such functions converts the solution of a given nonlinear differential equation to the solution of algebraic equations. Error analysis and convergence of the method is presented. Comparisons with the other methods reveal validity, applicability and great potential of the method. Several physical problems are treated to illustrative the good performance and high accuracy of the technique. (C) 2013 Elsevier Inc. All rights reserved.