A Step-by-Step Procedure for Local Analysis of Differential Equations

TL;DR

This paper presents a detailed algorithm for local perturbation analysis of differential equations, providing an analytical approach to equations from the theory of competing mechanisms, enhancing both theoretical understanding and practical application.

Contribution

It introduces a step-by-step procedure for local analysis of differential equations, bridging the gap between abstract exercises and practical solutions in complex models.

Findings

Provides an explicit analytical solution for a specific differential equation

Enhances understanding of local perturbation techniques in differential equations

Offers a practical algorithm suitable for graduate-level education

Abstract

This note provides a detailed algorithm to the application of local (perturbation) analysis of differential equations which is normally taught at graduate math courses. Exercise books often present more abstract and simplified versions of equations for the application of perturbation techniques. The equation we study comes from the theory of competing mechanisms and describes the behavior of rational buyers in a certain environment. While in the latter literature similar equations were solved numerically, an analytical solution adds both theoretical and practical value for students and researchers.