The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators, Koshmanenko Volodymyr, Dudkin Mykola

Автор: Holmes Mark H
Название: Introduction to Perturbation Methods
ISBN: 146145476X ISBN-13(EAN): 9781461454762
Издательство: Springer
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Описание: Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.One hundred new pages added including new material on transcedentally small terms, Kummer`s function, weakly coupled oscillators and wave interactions.

Автор: Adelaide B. Vasil`eva, Valentin F. Butuzov, Leonid
Название: The Boundary Function Method for Singular Perturbation Problems
ISBN: 0898713331 ISBN-13(EAN): 9780898713336
Издательство: Mare Nostrum (Eurospan)
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Цена: 101150.00 T
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Описание: This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. It contains a variety of original ideas and explicit calculations previously available only in journal literature, as well as many concrete applied problems illustrating the boundary function method algorithms.

Автор: Shishkin, Grigory I. , Shishkina, Lidia P.
Название: Difference Methods for Singular Perturbation Problems
ISBN: 0367386828 ISBN-13(EAN): 9780367386825
Издательство: Taylor&Francis
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Цена: 65320.00 T
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Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods.

The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. The authors develop a technique for constructing and justifying ε uniformly convergent difference schemes for boundary value problems with fewer restrictions on the problem data.

Containing information published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter. This part also studies both the solution and its derivatives with errors that are independent of the perturbation parameters.

Co-authored by the creator of the Shishkin mesh, this book presents a systematic, detailed development of approaches to construct ε uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems.

Автор: Wechselberger Martin
Название: Geometric Singular Perturbation Theory Beyond the Standard Form
ISBN: 3030363988 ISBN-13(EAN): 9783030363987
Издательство: Springer
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Описание: Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT).It is the first of its kind that introduces the GSPT in a coordinate-independent manner.

Автор: Miller J J H Et Al
Название: Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition)
ISBN: 9814390739 ISBN-13(EAN): 9789814390736
Издательство: World Scientific Publishing
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Описание: Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. It can be used as an introductory text to the theory underpinning fitted mesh methods.

Автор: J.K. Kevorkian; J.D. Cole
Название: Multiple Scale and Singular Perturbation Methods
ISBN: 0387942025 ISBN-13(EAN): 9780387942025
Издательство: Springer
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Цена: 158380.00 T
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Описание: Covers multiple scale and averaging methods. This book presents an account of the various perturbation techniques used in the sciences and engineering. It is suitable for a graduate text as well as a reference work on the subject.

Автор: Marchuk, Guri I. , Agoshkov, Valeri I. , Shutyae
Название: Adjoint Equations and Perturbation Algorithms in Nonlinear Problems
ISBN: 0367448580 ISBN-13(EAN): 9780367448585
Издательство: Taylor&Francis
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Описание: This book presents the theory of adjoint equations in nonlinear problems and their applications to perturbation algorithms for solution of nonlinear problems in mathematical physics. It formulates a series of principles of construction of adjoint operators in nonlinear problems.

Автор: K. W. Chang; F. A. Howes
Название: Nonlinear Singular Perturbation Phenomena
ISBN: 038796066X ISBN-13(EAN): 9780387960661
Издательство: Springer
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Описание: The presentation involves a study of both scalar and vector boundary value problems for ordinary dif- ferential equations, by means of the consistent use of differential in- equality techniques.

Автор: Robert E., Jr. O`Malley
Название: Singular Perturbation Methods for Ordinary Differential Equations
ISBN: 038797556X ISBN-13(EAN): 9780387975566
Издательство: Springer
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Цена: 130430.00 T
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Описание: Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir- ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places.

Автор: Volodymyr Koshmanenko
Название: Singular Quadratic Forms in Perturbation Theory
ISBN: 079235625X ISBN-13(EAN): 9780792356257
Издательство: Springer
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Цена: 102480.00 T
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Описание: Deals with the presentation of the method of singular quadratic forms in the perturbation theory of self-adjoint operators. This book interprets singular quadratic form in the role of an abstract boundary condition for self-adjoint extension. It also investigates various aspects of the singularity principle.

Автор: Johannes Sj?strand
Название: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
ISBN: 303010818X ISBN-13(EAN): 9783030108182
Издательство: Springer
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Описание: The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago.In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book.Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.

Автор: Tosio Kato
Название: Perturbation Theory for Linear Operators
ISBN: 354058661X ISBN-13(EAN): 9783540586616
Издательство: Springer
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Цена: 46570.00 T
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Описание: From the reviews: "[...] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.