Perturbation Methods In Applied Mathematics

Author : J. Kevorkian
Publisher : Springer Science & Business Media
ISBN 13 : 1475742134
Total Pages : 569 pages
Book Rating : 4.38/5 ( download)

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Download or read book Perturbation Methods in Applied Mathematics written by J. Kevorkian and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe matics, Ginn-Blaisdell, 1968. We present the material at a level which assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate level course on the subject. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B.

Author : J.K. Kevorkian
Publisher : Springer Science & Business Media
ISBN 13 : 1461239680
Total Pages : 642 pages
Book Rating : 4.80/5 ( download)

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Download or read book Multiple Scale and Singular Perturbation Methods written by J.K. Kevorkian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

Author : James A. Murdock
Publisher : SIAM
ISBN 13 : 9781611971095
Total Pages : 358 pages
Book Rating : 4.98/5 ( download)

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Download or read book Perturbations written by James A. Murdock and published by SIAM. This book was released on 1999-01-01 with total page 358 pages. 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.

Author : Robert E., Jr. O'Malley
Publisher : Springer Science & Business Media
ISBN 13 : 1461209773
Total Pages : 234 pages
Book Rating : 4.75/5 ( download)

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Download or read book Singular Perturbation Methods for Ordinary Differential Equations written by Robert E., Jr. O'Malley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. 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. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.

Author : E. J. Hinch
Publisher : Cambridge University Press
ISBN 13 : 9780521378970
Total Pages : 178 pages
Book Rating : 4.74/5 ( download)

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Download or read book Perturbation Methods written by E. J. Hinch and published by Cambridge University Press. This book was released on 1991-10-25 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.

Author : Anatoli V. Skorokhod
Publisher : Springer Science & Business Media
ISBN 13 : 0387224467
Total Pages : 500 pages
Book Rating : 4.66/5 ( download)

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Download or read book Random Perturbation Methods with Applications in Science and Engineering written by Anatoli V. Skorokhod and published by Springer Science & Business Media. This book was released on 2007-06-21 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.

Author : Carl M. Bender
Publisher : Springer Science & Business Media
ISBN 13 : 1475730691
Total Pages : 605 pages
Book Rating : 4.92/5 ( download)

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Download or read book Advanced Mathematical Methods for Scientists and Engineers I written by Carl M. Bender and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 0387283137
Total Pages : 332 pages
Book Rating : 4.35/5 ( download)

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Download or read book Methods and Applications of Singular Perturbations written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Author : Richard H. Rand
Publisher : Springer Science & Business Media
ISBN 13 : 1461210607
Total Pages : 254 pages
Book Rating : 4.03/5 ( download)

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Download or read book Perturbation Methods, Bifurcation Theory and Computer Algebra written by Richard H. Rand and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.

Author : Reza N. Jazar
Publisher : Springer Nature
ISBN 13 : 3030734625
Total Pages : 584 pages
Book Rating : 4.26/5 ( download)

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Download or read book Perturbation Methods in Science and Engineering written by Reza N. Jazar and published by Springer Nature. This book was released on 2021-07-12 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems.