Approximate Analytical Methods for Solving Ordinary Differential Equations

Introduction

Power Series Method
Introduction
Algebraic Method (Method of Undetermined Coefficients)
Solution at Ordinary Point of an Ordinary Differential Equation
Solution at a Singular Point (Regular) of an Ordinary
Differential Equation
Remarks on the Frobenius Solution at Irregular Singular Points
Taylor Series Method

Asymptotic Method
Introduction
Asymptotic Solutions at Irregular Singular Points at Infinity
Asymptotic Solutions of Perturbed Problems
Solutions to ODEs Containing a Large Parameter

Perturbation Techniques
Introduction
Regular Perturbation Theory
Singular Perturbation Theory

Method of Multiple Scales
Introduction
Method of Multiple Scales

WKB Theory
Introduction
WKB Approximation for Unperturbed Problems
WKB Approximation for Perturbed Problems

Nonperturbation Methods
Introduction
Lyapunov’s Artificial Small-Parameter Method
Delta Expansion Method
Adomian Decomposition Method

Homotopy Methods
Introduction
Homotopy Analysis Method
Homotopy Perturbation Method
Optimal Homotopy Analysis Method

Exercise Problems, Applications, and a Bibliography appear at the end of each chapter.