singular perturbation theory

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Singular Perturbation Theory

Author : Lindsay A. Skinner
ISBN : 1441999582
Genre : Mathematics
File Size : 89. 76 MB
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This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and is followed by four chapters of applications to ordinary differential equation problems of increasing complexity. Exercises are included as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems.

Singular Perturbation Theory

Author : Donald R. Smith
ISBN : 0521300428
Genre : Mathematics
File Size : 60. 22 MB
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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.

Singular Perturbation Theory

Author : R.S. Johnson
ISBN : 0387232176
Genre : Mathematics
File Size : 73. 63 MB
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The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.

Algebraic Analysis Of Singular Perturbation Theory

Author : Takahiro Kawai
ISBN : 0821835475
Genre : Mathematics
File Size : 20. 33 MB
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The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main approach used by the authors is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. The volume is suitable for graduate students and researchers interested in differential equations and special functions.

Problems In Singular Perturbation Theory

Author : James Alan Cochran
ISBN : STANFORD:36105011941965
Genre : Perturbation
File Size : 52. 46 MB
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A Study Of The Application Of Singular Perturbation Theory

Author : Raman K. Mehra
ISBN : NASA:31769000502974
Genre : Science
File Size : 49. 15 MB
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The Method Of Rigged Spaces In Singular Perturbation Theory Of Self Adjoint Operators

Author : Volodymyr Koshmanenko
ISBN : 9783319295350
Genre : Mathematics
File Size : 82. 3 MB
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This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadratic forms, and the theory of rigged Hilbert spaces. The book will appeal to researchers in mathematics and mathematical physics studying the scales of densely embedded Hilbert spaces, the singular perturbations phenomenon, and singular interaction problems.

Boundary Interior Layer Interactions In Nonlinear Singular Perturbation Theory

Author : Frederick A. Howes
ISBN : 9780821822036
Genre : Mathematics
File Size : 28. 60 MB
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Singular Perturbation Methods In Control

Author : Petar Kokotovic
ISBN : 9780898714449
Genre : Mathematics
File Size : 74. 96 MB
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This SIAM Classics edition of the 1986 book provides the theoretical foundation for representative control applications.

Analyzing Multiscale Phenomena Using Singular Perturbation Methods

Author : Jane Cronin
ISBN : 9780821809297
Genre : Mathematics
File Size : 34. 18 MB
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To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.

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