Asymptotic Methods for Ordinary Differential Equations

✍ Scribed by R. P. Kuzmina (auth.)

• Publisher: Springer Netherlands
• Year: 2000
• Tongue: English
• Leaves: 375
• Series: Mathematics and Its Applications 512
• Edition: 1
• Category: Library

✦ Synopsis

In this book we consider a Cauchy problem for a system of ordinary differential equations with a small parameter. The book is divided into th ree parts according to three ways of involving the small parameter in the system. In Part 1 we study the quasiregular Cauchy problem. Th at is, a problem with the singularity included in a bounded function j , which depends on time and a small parameter. This problem is a generalization of the regu­ larly perturbed Cauchy problem studied by Poincare [35]. Some differential equations which are solved by the averaging method can be reduced to a quasiregular Cauchy problem. As an example, in Chapter 2 we consider the van der Pol problem. In Part 2 we study the Tikhonov problem. This is, a Cauchy problem for a system of ordinary differential equations where the coefficients by the derivatives are integer degrees of a small parameter.

✦ Table of Contents

Front Matter....Pages i-x
Front Matter....Pages 1-2
Solution Expansions of the Quasiregular Cauchy Problem....Pages 3-82
The van der Pol Problem....Pages 83-128
Front Matter....Pages 129-130
The Boundary Functions Method....Pages 131-180
Proof of Theorems 28.1–28.4....Pages 181-230
The Method of Two Parameters....Pages 231-271
The Motion of a Gyroscope Mounted in Gimbals....Pages 272-305
Supplement....Pages 306-324
Front Matter....Pages 325-326
The Boundary Functions Method....Pages 327-349
The Method of Two Parameters....Pages 350-358
Back Matter....Pages 359-364

✦ Subjects

Ordinary Differential Equations