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Author :
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (317 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 : National Aeronautics and Space Administration (NASA)
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781723416996
Total Pages : 24 pages
Book Rating : 4.4/5 (169 download)
Download or read book Solution of Second-Order Linear System by Matched Asymptotic Expansions written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-21 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed. Ardema, M. D. Ames Research Center NASA-TM-84246, A-8938, NAS 1.15:84246 RTOP 307-01-00
Author :
Publisher : Elsevier
ISBN 13 : 0080871178
Total Pages : 153 pages
Book Rating : 4.0/5 (88 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 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matched Asymptotic Expansions and Singular Perturbations
Author : Augustin Fruchard
Publisher : Springer
ISBN 13 : 3642340350
Total Pages : 169 pages
Book Rating : 4.6/5 (423 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 : P.A. Lagerstrom
Publisher : Springer Science & Business Media
ISBN 13 : 1475719906
Total Pages : 263 pages
Book Rating : 4.4/5 (757 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 : Wolfgang Wasow
Publisher : Courier Dover Publications
ISBN 13 : 0486824586
Total Pages : 385 pages
Book Rating : 4.4/5 (868 download)
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
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Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (317 download)
Download or read book Solution of Linear Systems by a Singular Perturbation Technique written by and published by . This book was released on 1976 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Johannes Gualtherus van der Corput
Publisher :
ISBN 13 :
Total Pages : 356 pages
Book Rating : 4.X/5 (1 download)
Download or read book Asymptotic Expansions: The asymptotic behaviour of the real solutions of certain second order differential equations written by Johannes Gualtherus van der Corput and published by . This book was released on 1955 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mikhail Vasilʹevich Fedori︠u︡k
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (31 download)
Download or read book Asymptotic Expansions of Solutions of Differential Linear Equations of the Second Order in a Complex Domain written by Mikhail Vasilʹevich Fedori︠u︡k and published by . This book was released on 1969 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second order linear ordinary differential equations whose highest derivative is multiplied by a small parameter are solved by asymptotic series valid in unbounded domains and the connecting formulas across the Stokes lines are determined. (Author).
Author : Richard E. Meyer
Publisher : Academic Press
ISBN 13 : 1483264572
Total Pages : 418 pages
Book Rating : 4.4/5 (832 download)
Download or read book Singular Perturbations and Asymptotics written by Richard E. Meyer and published by Academic Press. This book was released on 2014-05-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics. The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications. The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations. The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.
Author : Arthur Erdélyi
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.3/5 (91 download)
Download or read book Asymptotic Solutions of Differential Equations with Transition Points written by Arthur Erdélyi and published by . This book was released on 1956 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frank W. J. Olver
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (25 download)
Download or read book Uniform Asymptotic Expansions of Solutions of Linear Second-order Differential Equations for Large Values of a Parameter written by Frank W. J. Olver and published by . This book was released on 1958 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. M. Ilʹin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821845615
Total Pages : 281 pages
Book Rating : 4.8/5 (456 download)
Download or read book Matching of Asymptotic Expansions of Solutions of Boundary Value Problems written by A. M. Ilʹin and published by American Mathematical Soc.. This book was released on 1992 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the solution of singularly perturbed boundary value problems for differential equations. It presents, for the first time, a detailed and systematic treatment of the version of the matching method developed by the author and his colleagues. A broad class of problems is considered from a unified point of view, and the procedure for constructing asymptotic expansions is discussed in detail. The book covers formal constructions of asymptotic expansions and provides rigorous justifications of these asymptotics. One highlight is a complete asymptotic analysis of Burger's equation with small diffusion in the neighborhood of the gradient catastrophe point. The book is suitable as a text for graduate study in asymptotic methods in calculus and singularly perturbed equations.
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Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.:/5 (3 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
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ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.:/5 (317 download)
Download or read book Numerical Integration of Asymptotic Solutions of Ordinary Differential Equations written by and published by . This book was released on 1989 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sergey G. Glebov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110382725
Total Pages : 460 pages
Book Rating : 4.1/5 (13 download)
Download or read book Oscillations and Resonances written by Sergey G. Glebov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-10 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators
Author : Frank W. J. Olver
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (665 download)
Download or read book Uniform Asymptotic Expansion of Solutions of Linear Second-order Differential Equations for Large Values of a Parameter written by Frank W. J. Olver and published by . This book was released on 1958 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
