R. P. Kuzmina

eBook, PDF

Asymptotic Methods for Ordinary Differential Equations (eBook, PDF)

Beschreibung

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.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 21.75MB

Barrierefreiheit

• Text-to-Speech

Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 364
• Erscheinungstermin: 29. Juni 2013
• Englisch
• ISBN-13: 9789401593472
• Artikelnr.: 44055261

Rezensionen

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)