Asymptotic methods for ordinary differential equations

Author(s)

    • Kuzmina, R. P.

Bibliographic Information

Asymptotic methods for ordinary differential equations

by R.P. Kuzmina

(Mathematics and its applications, v. 512)

Kluwer Academic, c2000

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Description and Table of Contents

Description

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

Preface. Part 1: The Quasiregular Cauchy Problem. 1. Solutions Expansions of the Quasiregular Cauchy Problem. 2. The Van der Pol Problem. Part 2: The Tikhonov 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. Part 3: The Double-Singular Cauchy Problem. 8. The Boundary Functions Method. 9. The Method of Two Parameters. Bibliography. Index.

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Details

  • NCID
    BA49006399
  • ISBN
    • 0792364007
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    x, 364 p.
  • Size
    25 cm
  • Parent Bibliography ID
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