Asymptotic methods for ordinary differential equations

著者

• Kuzmina, R. P.

書誌事項

Asymptotic methods for ordinary differential equations

by R.P. Kuzmina

（Mathematics and its applications, v. 512）

Kluwer Academic, c2000

内容説明・目次

内容説明

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.

目次

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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA49006399
• ISBN:
  • 0792364007
• 出版国コード: ne
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Dordrecht
• ページ数/冊数: x, 364 p.
• 大きさ: 25 cm
• 親書誌ID:
  • BA00044495