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Asymptotic Methods for Ordinary Differential Equations

Name: Asymptotic Methods for Ordinary Differential Equations
Brand: Springer Netherlands
SKU: 01974125
Price: 90.79 EUR
Availability: InStock
Author: R.P. Kuzmina
ISBN: 9789048155002

R.P. Kuzmina

Language

English

Book Paperback

Libristo code: 01974125

Publishers Springer Netherlands, November 2009

This book considers the Cauchy problem for a system of ordinary differential equations with a small... Full description

Libristo code: 01974125

222 b

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This book considers the Cauchy problem for a system of ordinary differential equations with a small parameter, filling in areas that have not been extensively covered in the existing literature. The well-known types of equations, such as the regularly perturbed Cauchy problem and the Tikhonov problem, are dealt with, but new ones are also treated, such as the quasiregular Cauchy problem, and the Cauchy problem with double singularity. For each type of problem, series are constructed which generalise the well-known series of Poincaré and Vasilyeva-Imanaliyev. It is shown that these series are asymptotic expansions of the solution, or converge to the solution on a segment, semiaxis or asymptotically large time intervals. Theorems are proved providing numerical estimates for the remainder term of the asymptotics, the time interval of the solution existence, and the small parameter values. Audience: This volume will be of interest to researchers and graduate students specialising in ordinary differential equations.