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Author :
Publisher : Elsevier
ISBN 13 : 0080871178
Total Pages : 144 pages
Book Rating : 4.72/5 ( download)
Download or read book Matched Asymptotic Expansions and Singular Perturbations written by and published by Elsevier. This book was released on 2011-08-26 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matched Asymptotic Expansions and Singular Perturbations
Author : P.A. Lagerstrom
Publisher : Springer Science & Business Media
ISBN 13 : 1475719906
Total Pages : 263 pages
Book Rating : 4.01/5 ( download)
Download or read book Matched Asymptotic Expansions written by P.A. Lagerstrom and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular perturba tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed further. Examples which required too sophis ticated and involved calculations, or advanced knowledge of a special field, are not treated; for instance, to the author's regret some very interesting applications to fluid mechanics had to be omitted for this reason. Artificial mathematical examples introduced to show some exotic or unexpected behavior are omitted, except when they are analytically simple and are needed to illustrate mathematical phenomena important for realistic problems. Problems of numerical analysis are not discussed.
Author : J.A. Leach
Publisher : Springer Science & Business Media
ISBN 13 : 0857293966
Total Pages : 289 pages
Book Rating : 4.61/5 ( download)
Download or read book Matched Asymptotic Expansions in Reaction-Diffusion Theory written by J.A. Leach and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.
Author : Augustin Fruchard
Publisher : Springer
ISBN 13 : 3642340350
Total Pages : 169 pages
Book Rating : 4.52/5 ( download)
Download or read book Composite Asymptotic Expansions written by Augustin Fruchard and published by Springer. This book was released on 2012-12-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.
Author :
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.81/5 ( download)
Download or read book Solution of Second-order Linear System by Matched Asymptotic Expansions written by and published by . This book was released on 1982 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. M. Ilʹin A. M. Il'in
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897348
Total Pages : 754 pages
Book Rating : 4.49/5 ( download)
Download or read book Matching of Asymptotic Expansions of Solutions of Boundary Value Problems written by A. M. Ilʹin A. M. Il'in and published by American Mathematical Soc.. This book was released on 1992 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M.V. Fedoryuk
Publisher : Springer Science & Business Media
ISBN 13 : 3642584233
Total Pages : 248 pages
Book Rating : 4.37/5 ( download)
Download or read book Partial Differential Equations V written by M.V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.
Author : Jean Cousteix
Publisher : Springer Science & Business Media
ISBN 13 : 3540464891
Total Pages : 437 pages
Book Rating : 4.91/5 ( download)
Download or read book Asymptotic Analysis and Boundary Layers written by Jean Cousteix and published by Springer Science & Business Media. This book was released on 2007-03-22 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.
Author : P. A. Lagerstrom
Publisher :
ISBN 13 : 9781475719918
Total Pages : 270 pages
Book Rating : 4.14/5 ( download)
Download or read book Matched Asymptotic Expansions written by P. A. Lagerstrom and published by . This book was released on 2014-01-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lindsay A. Skinner
Publisher : Springer Science & Business Media
ISBN 13 : 1441999582
Total Pages : 95 pages
Book Rating : 4.80/5 ( download)
Download or read book Singular Perturbation Theory written by Lindsay A. Skinner and published by Springer Science & Business Media. This book was released on 2011-05-11 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
