Asymptotic analysis of Emden-Fowler type equation with an application to power flow models

TL;DR

This paper analyzes a specific Emden-Fowler type equation arising in power flow models, establishing its asymptotic behavior and linking continuous and discrete solutions within electrical engineering applications.

Contribution

It provides the first asymptotic analysis of an Emden-Fowler equation in the context of power flow models, connecting mathematical physics with electrical engineering.

Findings

Discrete and continuous solutions share the same asymptotic behavior.

Properties of the continuous solution are characterized.

The analysis bridges Emden-Fowler equations and power flow modeling.

Abstract

Emden-Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden-Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model. Thus, we place Emden-Fowler type equations in the context of electrical engineering. We derive properties of the continuous solution of this specific Emden-Fowler type equation and study the asymptotic behavior of its discrete analog. We conclude that the discrete analog has the same asymptotic behavior as the classical continuous Emden-Fowler type equation that we consider.