Download or read book Asymptotic Solution of Systems of Linear Ordinary Differential Equations With Discontinuous Coefficients Classic Reprint written by Clive R. Chester and published by . This book was released on 2016-06-26 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Solution of Systems of Linear Ordinary Differential Equations with Discontinuous Coefficients written by Clive Ronald Chester and published by . This book was released on 1959 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Solution of Systems of Linear Ordinary Differential Equations with Discontinuous Coefficients written by Clive Ronald Chester and published by . This book was released on 1959 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Systems of Linear Ordinary Differential Equations Classic Reprint written by Herbert B. Keller and published by Forgotten Books. This book was released on 2018-05-04 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On Systems of Linear Ordinary Differential Equations The nearest approach to such a treatment is contained in the wkb method which yields an approximate solution of a linear second order equation as a sum of exponentials with variable coefficients and exponents. In some presentations of the method higher order approximations are also obtained, but it is generally not clear whether the successive approximations converge to a solution of the equation or not. For a large class of cond order equations involving a parameter in a particular way, Birkhoff and L ave settled this matter by showing that the web approximation is the leading term in an asymptotic expansion of the solution with respect to the parameter. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book An Asymptotic Solution of Linear Second Order Hyperbolic Differential Equations written by Morris Kline and published by Sagwan Press. This book was released on 2018-02-07 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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 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 Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations written by Ivan Kiguradze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of solutions are established, and some general theorems on the classification of equations according to their oscillatory properties are proved. In addition, the conditions are found under which nonlinear equations do not have singular, proper, oscillatory and monotone solutions. The book has five chapters: Chapter I deals with linear differential equations; Chapter II with quasilinear equations; Chapter III with general nonlinear differential equations; and Chapter IV and V deal, respectively, with higher-order and second-order differential equations of the Emden-Fowler type. Each section contains problems, including some which presently remain unsolved. The volume concludes with an extensive list of references. For researchers and graduate students interested in the qualitative theory of differential equations.
Download or read book Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems written by George David Birkhoff and published by . This book was released on 1908 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Solution of a Dispersive Hyperbolic Equation With Variable Coefficients Classic Reprint written by Norman Bleistein and published by Forgotten Books. This book was released on 2018-02-07 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Asymptotic Solution of a Dispersive Hyperbolic Equation With Variable Coefficients In the past few years there has been a great deal of interest in the asymptotic expansion of solutions of boundary value problems and initial boundary value problems for partial differential equations. These expansions are obtained for large distance and/or time or for large values of a parameter which may appear naturally in the equation and/or initial conditions, boundary conditions, etc. Many of these problems can be treated by a method in which special curves, called rays, in space or space-time plan an essential role. The asymptotic solution is determined in terms of amplitude and phase functions which satis fy ordinary differential equations on these rays. These equations can often be solved explicitly, so that the solution to the original problem is known if the initial values on the rays of the amplitude and phase functions are known. In some cases these initial values can be determined directly from the data initial conditions, boundary conditions, etc.) of the given problem, while in other situations an indirect method is necessary. This method involves the exact solution of a canonical problem i.a., a problem simpler than that given originally but having the same local features as the given problem. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Discontinuous Initial Value Problems and Asymptotic Expansion of Steady State Solutions Classic Reprint written by Robert M. Lewis and published by Forgotten Books. This book was released on 2015-07-28 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Discontinuous Initial Value Problems and Asymptotic Expansion of Steady-State Solutions Part II Asymptotic expansion of steady-state solutions of symmetric hyperbolic linear differential equations. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Differential Equations And Asymptotic Theory In Mathematical Physics written by Hua Chen and published by World Scientific. This book was released on 2004-10-18 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Richard Wasow and published by Dover Publications. This book was released on 1987 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Important scientific and scholarly titles previously unavailable- Sturdy hardcover volumes with sewn bindings and laminated covers- Prices well below those of comparable publications
Download or read book Asymptotic Methods in the Theory of Linear Differential Equations written by Stepan Fedorovich Feshchenko and published by . This book was released on 1967 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Asymptotic Methods for Ordinary Differential Equations written by R.P. Kuzmina and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we consider a Cauchy problem for a system of ordinary differential equations with a small parameter. The book is divided into th ree parts according to three ways of involving the small parameter in the system. In Part 1 we study the quasiregular Cauchy problem. Th at is, a problem with the singularity included in a bounded function j , which depends on time and a small parameter. This problem is a generalization of the regu larly perturbed Cauchy problem studied by Poincare [35]. Some differential equations which are solved by the averaging method can be reduced to a quasiregular Cauchy problem. As an example, in Chapter 2 we consider the van der Pol problem. In Part 2 we study the Tikhonov problem. This is, a Cauchy problem for a system of ordinary differential equations where the coefficients by the derivatives are integer degrees of a small parameter.
Download or read book Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations written by Valery V. Kozlov and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can’t be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.
