A new technique for solving singular IVPs of Emden-Fowler type

TL;DR

This paper introduces the optimal perturbation iteration method, a new analytical approach for solving singular Emden-Fowler type initial value problems, demonstrating high accuracy and adjustable convergence regions.

Contribution

The paper presents a novel perturbation iteration technique specifically designed for singular nonlinear differential equations, enhancing convergence control and solution accuracy.

Findings

Method shows high accuracy in solving Lane-Emden problems

Provides adjustable convergence regions for better solution control

Outperforms some existing analytical methods in effectiveness

Abstract

A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary.Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for nonlinear differential equations.