Introduction to Singular Perturbations

Robert E. Jr. O'Malley

• Publisher: Academic Press
• Year: 2012
• Print ISBN: 9780125259507
• eBook ISBN: 9780323162272
• Topic: Mathematics
• Subtopic: Number Theory
• Index: Mathematics

Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.

Table of contents

• Front Cover
• Introduction to Singular Perturbations
• Copyright Page
• Table of Contents
• Preface
• Chapter 1. First Concerns
• Chapter 2. The Regular Perturbation Method
• Chapter 3. Linear Boundary Value Problems
• Chapter 4. Nonlinear Initial Value Problems
• Chapter 5. Nonlinear Boundary Value Problems
• Chapter 6. The Singularly Perturbed Linear State Regulator Problem
• Chapter 7. Boundary Value Problems with Multiple Solutions Arising in Chemical Reactor Theory
• Chapter 8. Some Turning Point Problems
• References
• Index