Asymptotic Expansions For Ordinary Differential Equations
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Author | : Wolfgang Wasow |
Publisher | : Courier Dover Publications |
Total Pages | : 385 |
Release | : 2018-03-21 |
Genre | : Mathematics |
ISBN | : 0486824586 |
Download Asymptotic Expansions for Ordinary Differential Equations Book in PDF, Epub and Kindle
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.
Author | : Wolfgang Richard Wasow |
Publisher | : |
Total Pages | : 362 |
Release | : 1965 |
Genre | : Asymptotic expansions |
ISBN | : |
Download Asymptotic Expansions for Ordinary Differential Equations Book in PDF, Epub and Kindle
Author | : Augustin Fruchard |
Publisher | : Springer |
Total Pages | : 169 |
Release | : 2012-12-15 |
Genre | : Mathematics |
ISBN | : 3642340350 |
Download Composite Asymptotic Expansions Book in PDF, Epub and Kindle
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 | : |
Total Pages | : |
Release | : 1965 |
Genre | : |
ISBN | : |
Download ASYMPTOTIC EXPANSIONS FOR ORDINARY DIFFERENTIAL EQUATIONS Book in PDF, Epub and Kindle
Author | : A. Erdélyi |
Publisher | : Courier Corporation |
Total Pages | : 118 |
Release | : 2012-04-27 |
Genre | : Mathematics |
ISBN | : 0486155056 |
Download Asymptotic Expansions Book in PDF, Epub and Kindle
Various methods for asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansion.
Author | : P.A. Lagerstrom |
Publisher | : Springer Science & Business Media |
Total Pages | : 263 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475719906 |
Download Matched Asymptotic Expansions Book in PDF, Epub and Kindle
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 | : E. T. Copson |
Publisher | : Cambridge University Press |
Total Pages | : 136 |
Release | : 2004-06-03 |
Genre | : Mathematics |
ISBN | : 9780521604826 |
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Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.
Author | : |
Publisher | : Elsevier |
Total Pages | : 153 |
Release | : 2011-08-26 |
Genre | : Mathematics |
ISBN | : 0080871178 |
Download Matched Asymptotic Expansions and Singular Perturbations Book in PDF, Epub and Kindle
Matched Asymptotic Expansions and Singular Perturbations
Author | : Mikhail V. Fedoryuk |
Publisher | : Springer Science & Business Media |
Total Pages | : 370 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642580165 |
Download Asymptotic Analysis Book in PDF, Epub and Kindle
In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Author | : Carlos Simpson |
Publisher | : Springer |
Total Pages | : 144 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 354046641X |
Download Asymptotic Behavior of Monodromy Book in PDF, Epub and Kindle
This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.