Polytropic Dynamical Systems with Time Singularity

TL;DR

This paper studies a class of second order singular differential equations modeling astrophysical phenomena, proposing a hybrid numerical method to approximate their solutions.

Contribution

It introduces a novel hybrid method specifically designed for Lane-Emden-type equations with time singularities.

Findings

Effective approximation of solutions demonstrated

Applicable to astrophysical models like stellar structures

Improves numerical stability over existing methods

Abstract

In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model phenomena in astrophysics such as stellar structure and are governed by polytropics with applications in isothermal gas spheres. A hybrid method is proposed to approximate the solution of this type of dynamic equations.