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Introduction to the General Theory of Singular Perturbations

Mathematics
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Book Rating : 416/5 ( reviews)

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Book Synopsis Introduction to the General Theory of Singular Perturbations by : S. A. Lomov

Download or read book Introduction to the General Theory of Singular Perturbations written by S. A. Lomov. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.

Methods and Applications of Singular Perturbations

2006-06-04 Mathematics
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Release : 2006-06-04
Genre : Mathematics
Kind : eBook
Book Rating : 137/5 ( reviews)

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Book Synopsis Methods and Applications of Singular Perturbations by : Ferdinand Verhulst

Download or read book Methods and Applications of Singular Perturbations written by Ferdinand Verhulst. This book was released on 2006-06-04. Available in PDF, EPUB and Kindle. Book excerpt: Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Singular-Perturbation Theory

1985-08-30 Mathematics
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Release : 1985-08-30
Genre : Mathematics
Kind : eBook
Book Rating : 421/5 ( reviews)

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Book Synopsis Singular-Perturbation Theory by : Donald R. Smith

Download or read book Singular-Perturbation Theory written by Donald R. Smith. This book was released on 1985-08-30. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to singular perturbation problems. Since the nature of the nonuniformity can vary from case to case, the author considers and solves a variety of problems, mostly for ordinary differential equations.

The Theory of Singular Perturbations

1996-11-08 Mathematics
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Release : 1996-11-08
Genre : Mathematics
Kind : eBook
Book Rating : 751/5 ( reviews)

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Book Synopsis The Theory of Singular Perturbations by : E.M. de Jager

Download or read book The Theory of Singular Perturbations written by E.M. de Jager. This book was released on 1996-11-08. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathematical justification of these methods. The latter implies a priori estimates of solutions of differential equations; this involves the application of Gronwall's lemma, maximum principles, energy integrals, fixed point theorems and Gåding's theorem for general elliptic equations. These features make the book of value to mathematicians and researchers in the engineering sciences, interested in the mathematical justification of formal approximations of solutions of practical perturbation problems. The text is selfcontained and each chapter is concluded with some exercises.

Perturbations

1999-01-01 Mathematics
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Release : 1999-01-01
Genre : Mathematics
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Book Rating : 095/5 ( reviews)

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Book Synopsis Perturbations by : James A. Murdock

Download or read book Perturbations written by James A. Murdock. This book was released on 1999-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.

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