Approximate solutions to a nonlinear functional differential equation

TL;DR

This paper investigates a nonlinear functional differential equation related to the logistic equation, using numerical and perturbation methods to identify parameter regions where solutions can be approximated by linear solutions, and maps the solution space.

Contribution

It introduces a combined numerical and perturbation approach to approximate solutions and maps the solution space for a class of nonlinear functional differential equations.

Findings

Parameter regions where linear solutions approximate nonlinear solutions well

Identification of solution spaces using continuation methods

Enhanced understanding of nonlinear functional differential equations

Abstract

A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by known series solutions of the linear version of the equation. The solution space for a particular class of functions is then mapped out using a continuation approach.