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 Society(RI). This book was released on 2014-09-11 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
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
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:
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:
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.
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:
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).
Download or read book Asymptotic Behavior and Stability Problems in Ordinary Differential Equations written by Lamberto Cesari and published by Springer. This book was released on 2013-11-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call "qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
Download or read book Asymptotics of Linear Differential Equations written by M.H. Lantsman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.
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:
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.
Download or read book Asymptotic Analysis of Solutions of Almost Diagonal Systems of Ordinary Linear Differential Equations at a Turning Point written by Roy Yue-Wing Lee and published by . This book was released on 1967 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Turning Point for Certain Systems of Linear Differential Equations written by Tadepalli Ventata Subrahmanya Lakshmi Narasimnha Sastry and published by . This book was released on 1965 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
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:
Download or read book The Asymptotic Solution of Linear Differential Systems written by Michael Stephen Patrick Eastham and published by Oxford University Press, USA. This book was released on 1989 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account from 1975-1988 of the developments in the application of the modern asymptotic theory of linear differential systems, which dates from the Levinson Theorem of 1948. The main results and techniques are identified and earlier results are placed in a wider context.
