Asymptotic Expansions for Ordinary Differential Equations

Asymptotic Expansions for Ordinary Differential Equations
Author: Wolfgang Wasow
Publisher: Courier Dover Publications
Total Pages: 385
Release: 2018-03-21
Genre: Mathematics
ISBN: 0486824586

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.

Matched Asymptotic Expansions

Matched Asymptotic Expansions
Author: P.A. Lagerstrom
Publisher: Springer Science & Business Media
Total Pages: 263
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475719906

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.

Asymptotic Expansions

Asymptotic Expansions
Author: A. Erdélyi
Publisher: Courier Corporation
Total Pages: 118
Release: 1956-01-01
Genre: Mathematics
ISBN: 0486603180

Originally prepared for the Office of Naval Research, this important monograph introduces various methods for the asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansions. Author's preface. Bibliography.

Asymptotic Expansions

Asymptotic Expansions
Author: E. T. Copson
Publisher: Cambridge University Press
Total Pages: 136
Release: 2004-06-03
Genre: Mathematics
ISBN: 9780521604826

Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.

Solving Ordinary Differential Equations II

Solving Ordinary Differential Equations II
Author: Ernst Hairer
Publisher: Springer Science & Business Media
Total Pages: 615
Release: 2013-03-14
Genre: Mathematics
ISBN: 3662099470

"Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge braic equations. It contains three chapters: Chapter IV on one-step (Runge Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.

Asymptotics and Borel Summability

Asymptotics and Borel Summability
Author: Ovidiu Costin
Publisher: CRC Press
Total Pages: 266
Release: 2008-12-04
Genre: Mathematics
ISBN: 1420070320

Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr

Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations

Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations
Author: Ivan Kiguradze
Publisher: Springer
Total Pages: 331
Release: 1992-11-30
Genre: Mathematics
ISBN: 079232059X

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.

Asymptotic Behavior and Stability Problems in Ordinary Differential Equations

Asymptotic Behavior and Stability Problems in Ordinary Differential Equations
Author: Lamberto Cesari
Publisher: Springer
Total Pages: 278
Release: 2013-11-09
Genre: Mathematics
ISBN: 3662403684

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.

Asymptotic Integration of Differential and Difference Equations

Asymptotic Integration of Differential and Difference Equations
Author: Sigrun Bodine
Publisher: Springer
Total Pages: 411
Release: 2015-05-26
Genre: Mathematics
ISBN: 331918248X

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.

Basic Theory of Ordinary Differential Equations

Basic Theory of Ordinary Differential Equations
Author: Po-Fang Hsieh
Publisher: Springer Science & Business Media
Total Pages: 480
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461215064

Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.