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Asymptotic Methods for Ordinary Differential Equations

  • Book
  • © 2000

Overview

Authors:
  1. R. P. Kuzmina

    1. Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow, Russia

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
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  2. The Quasiregular Cauchy Problem

    1. Front Matter

      Pages 1-2
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    2. Solution Expansions of the Quasiregular Cauchy Problem

      • R. P. Kuzmina
      Pages 3-82

    3. The van der Pol Problem

      • R. P. Kuzmina
      Pages 83-128

  3. The Tikhonov Problem

    1. Front Matter

      Pages 129-130
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    2. The Boundary Functions Method

      • R. P. Kuzmina
      Pages 131-180

    3. Proof of Theorems 28.1–28.4

      • R. P. Kuzmina
      Pages 181-230

    4. The Method of Two Parameters

      • R. P. Kuzmina
      Pages 231-271

    5. The Motion of a Gyroscope Mounted in Gimbals

      • R. P. Kuzmina
      Pages 272-305

    6. Supplement

      • R. P. Kuzmina
      Pages 306-324

  4. The Double-Singular Cauchy Problem

    1. Front Matter

      Pages 325-326
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    2. The Boundary Functions Method

      • R. P. Kuzmina
      Pages 327-349

    3. The Method of Two Parameters

      • R. P. Kuzmina
      Pages 350-358

  5. Back Matter

    Pages 359-364
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow, Russia

    R. P. Kuzmina

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

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 2000

  • Hardcover ISBN: 978-0-7923-6400-9Published: 30 September 2000

  • Softcover ISBN: 978-90-481-5500-2Published: 15 December 2010

  • eBook ISBN: 978-94-015-9347-2Published: 29 June 2013

  • Edition Number: 1

  • Number of Pages: X, 364

  • Topics: Ordinary Differential Equations

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