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© 2000

Asymptotic Methods for Ordinary Differential Equations

Book

Part of the Mathematics and Its Applications book series (MAIA, volume 512)

Table of contents

  1. Front Matter
    Pages i-x
  2. The Quasiregular Cauchy Problem

    1. Front Matter
      Pages 1-2
    2. R. P. Kuzmina
      Pages 83-128
  3. The Tikhonov Problem

    1. Front Matter
      Pages 129-130
    2. R. P. Kuzmina
      Pages 131-180
    3. R. P. Kuzmina
      Pages 181-230
    4. R. P. Kuzmina
      Pages 231-271
    5. R. P. Kuzmina
      Pages 272-305
    6. R. P. Kuzmina
      Pages 306-324
  4. The Double-Singular Cauchy Problem

    1. Front Matter
      Pages 325-326
    2. R. P. Kuzmina
      Pages 327-349
    3. R. P. Kuzmina
      Pages 350-358
  5. Back Matter
    Pages 359-364

About this book

Introduction

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.

Keywords

Cauchy problem differential equation ordinary differential equation

Authors and affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow Lomonosov State UniversityMoscowRussia

Bibliographic information

  • Book Title Asymptotic Methods for Ordinary Differential Equations
  • Authors R.P. Kuzmina
  • Series Title Mathematics and Its Applications
  • DOI https://doi.org/10.1007/978-94-015-9347-2
  • Copyright Information Springer Science+Business Media B.V. 2000
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-7923-6400-9
  • Softcover ISBN 978-90-481-5500-2
  • eBook ISBN 978-94-015-9347-2
  • Edition Number 1
  • Number of Pages X, 364
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Ordinary Differential Equations
  • Buy this book on publisher's site

Reviews

From the reviews:

"The book is devoted to the study of the Cauchy problem for the systems of ordinary differential equations … . We emphasize, finally, that the book contains many explicitly or analytically or numerically solved examples. Summarizing it is an interesting and well-written book that provides good estimates to the solution of the Cauchy problem posed for the systems of very general nonlinear ODE-s. It will be useful for anyone interested in analysis, especially to specialists in ODE-s, physicists, engineers and students … .” (Jeno Hegedus, Acta Scientiarum Mathematicarum, Vol. 74, 2008)