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Author :
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (897 download)
Download or read book Asymptotic Solutions of Differential Equations with Turning Points written by and published by . This book was released on 1953 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. C. Thorne
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Asymptotic Solution of Differential Equations with a Turning Point and Singularities written by R. C. Thorne and published by . This book was released on 1957 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wallace Eugene Johnson
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.:/5 (89 download)
Download or read book Asymptotic Solutions of a Linear Second Order Differential Equation with Two Turning Points written by Wallace Eugene Johnson and published by . This book was released on 1952 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudolph Ernest Langer
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.X/5 (1 download)
Download or read book On the Asymptotic Solutions of Ordinary Linear Differential Equations about a Turning Point written by Rudolph Ernest Langer and published by . This book was released on 1954 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wolfgang Wasow
Publisher : Springer Science & Business Media
ISBN 13 : 1461210909
Total Pages : 255 pages
Book Rating : 4.4/5 (612 download)
Download or read book Linear Turning Point Theory written by Wolfgang Wasow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: My book "Asymptotic Expansions for Ordinary Differential Equations" published in 1965 is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present state of knowledge of all the topics discussed there could not be fitted into one volume without resorting to an excessively terse style of writing. Instead of undertaking such a task, I have concentrated, in this exposi tion, on the aspects of the asymptotic theory with which I have been particularly concerned during those 20 years, which is the nature and structure of turning points. As in Chapter VIII of my previous book, only linear analytic differential equations are considered, but the inclusion of important new ideas and results, as well as the development of the neces sary background material have made this an exposition of book length. The formal theory of linear analytic differential equations without a parameter near singularities with respect to the independent variable has, in recent years, been greatly deepened by bringing to it methods of modern algebra and topology. It is very probable that many of these ideas could also be applied to the problems concerning singularities with respect to a parameter, and I hope that this will be done in the near future. It is less likely, however, that the analytic, as opposed to the formal, aspects of turning point theory will greatly benefit from such an algebraization.
Author : Shlomo Strelitz
Publisher : American Mathematical Soc.
ISBN 13 : 0821813528
Total Pages : 105 pages
Book Rating : 4.8/5 (218 download)
Download or read book Asymptotics for Solutions of Linear Differential Equations Having Turning Points with Applications written by Shlomo Strelitz and published by American Mathematical Soc.. This book was released on 1999 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotics are built for the solutions $y_j(x, \lambda)$, $y_j DEGREES{(k)}(0, \lambda)=\delta_{j\, n-k}$, $0\le j, k+1\le n$ of the equation $L(y)=\lambda p(x)y, \quad x\in [0,1], $ where $L(y)$ is a linear differential operator of whatever order $n\ge 2$ and $p(x)$ is assumed to possess a finite number of turning points. The established asymptotics are afterwards applied to the study of: 1) the existence of infinite eigenvalue sequences for various multipoint boundary problems posed on $L(y)=\lambda p(x)y, \quad x\in [0,1], $, especially as $n=2$ and $n=3$ (let us be aware that the same method can be successfully applied on many occasions in case $n>3$ too) and 2) asymptotical distribution of the corresponding eigenvalue sequences on the
Author : Mikhail V. Fedoryuk
Publisher : Springer Science & Business Media
ISBN 13 : 3642580165
Total Pages : 370 pages
Book Rating : 4.6/5 (425 download)
Download or read book Asymptotic Analysis written by Mikhail V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : RUDOLPH E. LANGER
Publisher :
ISBN 13 :
Total Pages : 1 pages
Book Rating : 4.:/5 (227 download)
Download or read book The Construction of Related Equations for the Asymptotic Theory of Linear Ordinary Differential Equations about a Turning Point written by RUDOLPH E. LANGER and published by . This book was released on 1962 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully developed theory is extant, and can justifiably be referred to as classical, for the determination of the asymptotic forms of the solutions of a differential equation over any closed zregion which completely excludes turning-points. This theory applies, of course, irrespective of the region, to all equations with constant coefficients. The state of the theory is very different, namely quite fragmentary, when a turningpoint is lodged within the region. For this reason, and also because modern physical theories require it, the stdy of the solution forms of an equation in a region about a turning-point is of emminent contemporary interest. The classical algorithms fail irretrievably in such a region, a fact which has been shown to be inevitable by results otherwise obtained, because the forms yielded by those algorithms lak adequacy to reflect the intricate functional metamorphoses which characterize the solutions of the differential equation in a turning-point neighborhood. The origin is in this case a turning point, and bout this point the solutions undergo transitions between oscillatory and exponential function types. (Author).
Author : Nicholas D. Kazarinoff
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.3/5 (91 download)
Download or read book Asymptotic Solution of Ordinary Differential Equations written by Nicholas D. Kazarinoff and published by . This book was released on 1959 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The project has supported the investigation of three mathematical problems: a Peano-like existence proof for solutions of the Goursat problem for quasi-linear equations has been found, a Runge-Kutta process for the numerical solution of this problem has been developed, and the asymtotic behavior of solutions of ordinary linear differential equations having two simple turning points has been determined.
Author : E. W. Montroll
Publisher :
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.:/5 (16 download)
Download or read book On the Asymptotic Solutions of Ordinary Linear Differential Equations about a Turning Point written by E. W. Montroll and published by . This book was released on 1952 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Leonard Evans
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.:/5 (319 download)
Download or read book Asymptotic Solutions in the Neighborhood of a Turning Point for Linear Ordinary Differential Equations Containing a Parameter written by Robert Leonard Evans and published by . This book was released on 1951 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : White Roscoe B
Publisher : World Scientific
ISBN 13 : 1911298593
Total Pages : 432 pages
Book Rating : 4.9/5 (112 download)
Download or read book Asymptotic Analysis Of Differential Equations (Revised Edition) written by White Roscoe B and published by World Scientific. This book was released on 2010-08-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
Author : Naofumi Honda
Publisher : Springer
ISBN 13 : 4431557024
Total Pages : 133 pages
Book Rating : 4.4/5 (315 download)
Download or read book Virtual Turning Points written by Naofumi Honda and published by Springer. This book was released on 2015-07-07 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi–Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary.
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 : Calvin Hayden Wilcox
Publisher :
ISBN 13 :
Total Pages : 268 pages
Book Rating : 4.:/5 (43 download)
Download or read book Asymptotic Solutions of Differential Equations and Their Applications written by Calvin Hayden Wilcox and published by . This book was released on 1964 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudolph Ernest Langer
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (952 download)
Download or read book On the Asymptotic Solutions of Ordinary Linear Differential Equations about a Turning Point written by Rudolph Ernest Langer and published by . This book was released on 1858 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
