Solving third-order Lane–Emden–Fowler equations using a variable stepsize formulation of a pair of block methods.

Abstract

[EN]This manuscript presents a variable stepsize formulation of a pair of block methods to efficiently solve third-order IVP models of Lane–Emden–Fowler type equations. The main method is obtained considering two intermediate points. This method combines an appropriate set of formulas for dealing with the singularity at the left endpoint . The proposed method is implemented in variable step-size mode to ensure that the truncation error is kept within a specified tolerance. The results of the numerical experiments confirm the good performance of the variable step-size implementation presented in this paper.