Asymptotic Expansion Method for Singular
Perturbation Problem

Abstract

The main purpose of this thesis is to address the application of perturbation expansion techniques for the solution perturbed problems, precisely differential equations. When a large or small parameter ‘"’ known as the perturbation parameter occurs in a mathematical
model, then the model problem is known as a perturbed problem. Asymptotic expansion technique is a method to get the approximate solution using asymptotic series
for model perturbed problems. The asymptotic series may not and often do not converge but in a truncated form of only two or three terms, provide a useful approximation to the
original problem. Though the perturbed differential equations can be solved numerically by using various numerical schemes, but the asymptotic techniques provide an awareness of the solution before one compute the numerical solution. Here, perturbation expansion for some model algebraic and differential equations are considered and the results are compared with the exact solution.