Download or read book Asymptotic Treatment of Differential Equations written by A. Georgescu and published by CRC Press. This book was released on 1995-05-15 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main definitions and results of asymptotic analysis and the theory of regular and singular perturbations are summarized in this book. They are applied to the asymptotic study of several mathematical models from mechanics, fluid dynamics, statistical mechanics, meteorology and elasticity. Due to the generality of presentation this applications-oriented book is suitable for the solving of differential equations from any other field of interest.
Download or read book Asymptotic Analysis of Differential Equations written by R. B. White and published by World Scientific. This book was released on 2010 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
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.
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 Integration of Differential and Difference Equations written by Sigrun Bodine and published by Springer. This book was released on 2015-05-26 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.
Download or read book Introduction To Asymptotics A Treatment Using Nonstandard Analysis written by Douglas S Jones and published by World Scientific. This book was released on 1997-01-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hyperasymptotics as well as uniform asymptotics. There are many numerical examples to illustrate the relation between theory and practice. Exercises in the chapters enable the book to be used as a text for an introductory course.
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 Analysis and the Numerical Solution of Partial Differential Equations written by Hans G. Kaper and published by CRC Press. This book was released on 1991-02-25 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
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 Impulsive Differential Equations Asymptotic Properties Of The Solutions written by Drumi D Bainov and published by World Scientific. This book was released on 1995-03-29 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Download or read book Asymptotic Behavior of Solutions of Differential Difference Equations written by Richard Bellman and published by American Mathematical Soc.. This book was released on 1959 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Issues For Some Partial Differential Equations Second Edition written by Michel Marie Chipot and published by World Scientific. This book was released on 2024-04-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Download or read book Introduction to Asymptotics written by Douglas Samuel Jones and published by World Scientific. This book was released on 1997 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A very attractive feature of the book is the numerous examples illustrating the methods. A fine collection of exercises enriches each chapter, challenging the reader to check his progress in understanding the methods".Mathematical Reviews"As an introductory book to asymptotics, with chapters on uniform asymptotics and exponential asymptotics, this book clearly fills a gap it has a friendly size and contains many convincing numerical examples and interesting exercises. Hence, I recommend the book to everyone who works in asymptotics".SIAM, 1998" it is an excellent book that contains interesting results and methods for the researchers. It will be useful for the students interested in analysis and lectures on asymptotic methods The reviewer recommends the book to everyone who is interested in analysis, engineers and specialists in ODE-s"Acta Sci. Math. (Szeged), 1999
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 and Numerical Methods for Partial Differential Equations with Critical Parameters written by H.G. Kaper and published by Springer. This book was released on 2012-10-16 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.
Download or read book Some Asymptotic Problems in the Theory of Partial Differential Equations written by O. A. Oleĭnik and published by Cambridge University Press. This book was released on 1996-03-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more.
Download or read book Asymptotic Behavior of Monodromy written by Carlos Simpson and published by Springer. This book was released on 1991 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
