Singular Perturbation Theory

Mathematical and Analytical Techniques with Applications to Engineering

Author: R.S. Johnson

Publisher: Springer Science & Business Media

ISBN: 9780387232171

Category: Mathematics

Page: 292

View: 6196

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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.
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Approximate Analytical Methods for Solving Ordinary Differential Equations

Author: T.S.L Radhika,T. K.V. Iyengar,T. Raja Rani

Publisher: CRC Press

ISBN: 1466588160

Category: Mathematics

Page: 200

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Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods. The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete description of the methods without going deep into rigorous mathematical aspects. Detailed examples illustrate the application of the methods to solve real-world problems. The authors introduce the classical power series method for solving differential equations before moving on to asymptotic methods. They next show how perturbation methods are used to understand physical phenomena whose mathematical formulation involves a perturbation parameter and explain how the multiple-scale technique solves problems whose solution cannot be completely described on a single timescale. They then describe the Wentzel, Kramers, and Brillown (WKB) method that helps solve both problems that oscillate rapidly and problems that have a sudden change in the behavior of the solution function at a point in the interval. The book concludes with recent nonperturbation methods that provide solutions to a much wider class of problems and recent analytical methods based on the concept of homotopy of topology.
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Methods and Applications of Singular Perturbations

Boundary Layers and Multiple Timescale Dynamics

Author: Ferdinand Verhulst

Publisher: Springer Science & Business Media

ISBN: 0387283137

Category: Mathematics

Page: 328

View: 6624

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Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
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Theory of Stochastic Differential Equations with Jumps and Applications

Mathematical and Analytical Techniques with Applications to Engineering

Author: Rong SITU

Publisher: Springer Science & Business Media

ISBN: 0387251758

Category: Mathematics

Page: 434

View: 2418

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Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
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Inverse Problems

Mathematical and Analytical Techniques with Applications to Engineering

Author: Alexander G. Ramm

Publisher: Springer Science & Business Media

ISBN: 0387232184

Category: Mathematics

Page: 442

View: 6345

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Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
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Singular Perturbation Methods in Control

Analysis and Design

Author: Petar Kokotovic,Hassan K. Khali,John O'Reilly

Publisher: SIAM

ISBN: 0898714443

Category: Mathematics

Page: 371

View: 6108

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This SIAM Classics edition of the 1986 book provides the theoretical foundation for representative control applications.
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Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

Author: Carl M. Bender,Steven A. Orszag

Publisher: Springer Science & Business Media

ISBN: 9780387989310

Category: Mathematics

Page: 593

View: 1780

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A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
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Singular-Perturbation Theory

An Introduction with Applications

Author: Donald R. Smith

Publisher: Cambridge University Press

ISBN: 9780521300421

Category: Mathematics

Page: 500

View: 3355

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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.
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