Overview

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 Poincare 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.

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9789048155002

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Reviews

"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)"

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)

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)

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)

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