Group classification of second order neutral differential equations

TL;DR

This paper develops a symmetry-based classification method for second order neutral differential equations, providing a comprehensive group classification that was previously unavailable in the literature.

Contribution

It introduces a complete group classification of second order linear neutral differential equations and their delay counterparts using Lie symmetry methods.

Findings

Complete group classification of second order linear neutral differential equations

Group classification of second order linear delay differential equations

Application of Lie symmetry methods to neutral differential equations

Abstract

In this paper, we discuss the method of obtaining symmetries for second order nonhomogeneous neutral differential equations with variable coefficients. We use Taylor theorem for a function of several variables to obtain a Lie type invariance condition and the determining equations. Further we make a complete group classification of the second order linear neutral differential equation, for which there is no existing literature. As a special case, we present a complete group classification of the corresponding second order linear delay differential equation.