Asymptotic Methods for Ordinary Differential Equations

2000
ISBN: 978-0-7923-6400-9
Verlag: Springer Netherlands

Buch, Englisch, Band 512, 364 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1560 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Kuzmina, R. P.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

1. Solution Expansions of the Quasiregular Cauchy Problem.- 2. The van der Pol Problem.- 3. The Boundary Functions Method.- 4. Proof of Theorems 28.1–28.4.- 5. The Method of Two Parameters.- 6. The Motion of a Gyroscope Mounted in Gimbals.- 7. Supplement.- 8. The Boundary Functions Method.- 9. The Method of Two Parameters.