Analytic solution of system of singular nonlinear differential equations with Neumann-Robin boundary conditions arising in astrophysics

TL;DR

This paper introduces a new analytic method combining Green's function and homotopy analysis to solve nonlinear differential systems with boundary conditions relevant in astrophysics, offering improved accuracy and convergence control.

Contribution

The paper presents a novel approach that integrates Green's function with homotopy analysis for solving nonlinear differential equations with boundary conditions, enhancing convergence and accuracy.

Findings

Method outperforms existing iterative techniques.

Provides convergence and error estimates.

Demonstrates high accuracy through examples.

Abstract

In this paper, we propose a new approach for the approximate analytic solution of system of Lane-Emden-Fowler type equations with Neumann-Robin boundary conditions. The algorithm is based on Green's function and the homotopy analysis method. This approach depends on constructing Green's function before establishing the recursive scheme for the approximate analytic solution of the equivalent system of integral equations. Unlike Adomian decomposition method (ADM) \cite{singh2020solving}, the present method contains adjustable parameters to control the convergence of the approximate series solution. Convergence and error estimation of the present is provided under quite general conditions. Several examples are considered to demonstrate the accuracy of the current algorithm. Computational results reveal that the proposed approach produces better results as compared to some existing iterative methods.