Asymptotic Methods for Ordinary Differential Equations

ISBN-13: 9780792364009 / Angielski / Twarda / 2000 / 364 str.

R. P. Kuzmina

Opis

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."

Recenzje

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)

Spis treści

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.