Search Results: asymptotic-analysis-of-differential-equations

Asymptotic Analysis of Differential Equations

Author: R. B. White

Publisher: World Scientific

ISBN: 1848166079

Category: Mathematics

Page: 405

View: 6526

"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.

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Author: Hans G. Kaper,Marc Garbey

Publisher: CRC Press

ISBN: 9780585319674

Category: Mathematics

Page: 286

View: 9976

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

Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations

Author: Anatoliy M Samoilenko,Oleksandr Stanzhytskyi

Publisher: World Scientific

ISBN: 981446239X

Category: Mathematics

Page: 324

View: 482

Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed. Contents:Differential Equations with Random Right-Hand Sides and Impulsive EffectsInvariant Sets for Systems with Random PerturbationsLinear and Quasilinear Stochastic Ito SystemsExtensions of Ito Systems on a TorusThe Averaging Method for Equations with Random Perturbations Readership: Graduate students and researchers in mathematics and physics. Keywords:Stochastic Systems;Invariant Manifold;Invariant Torus;Lyapunov Function;Stability;Periodic Solutions;Reduction PrincipleKey Features:Develops new methods of studying the stochastic differential equations; contrary to the existing purely probabilistic methods, these methods are based on the differential equations approachStudies new classes of stochastic systems, for instance, the stochastic expansions of dynamical systems on the torus, enabling the study of general oscillatory systems subject to the influences of random factorsBridges the gap between the stochastic differential equations and ordinary differential equations, namely, it describes which properties of the ordinary differential equations remain unchanged, and which new properties appear in the stochastic caseReviews: "This book is well written and readable. Most results included in the book are by the authors. All chapters contain a final section with comments and references, where the authors make a detailed description of the origin of the results. This is a helpful point for all readers, especially for researchers in the field." Mathematical Reviews "This monograph collects a great variety of stimulating results concerning random perturbation theory always deeply rooted in the classical theory of ordinary differential equations and celestial mechanics. Despite its technical content the text is written in a clear and accessible way, with many insightful explanations. The fact that each chapter closes with a detailed review on the current literature and the historic development of the theory is highly appreciated." Zentralblatt MATH

Asymptotic Analysis

Linear Ordinary Differential Equations

Author: Mikhail V. Fedoryuk

Publisher: Springer Science & Business Media

ISBN: 3642580165

Category: Mathematics

Page: 363

View: 8570

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.

Differential Equations, Asymptotic Analysis, and Mathematical Physics

Author: Michael Demuth,Bert-Wolfgang Schulze

Publisher: John Wiley & Sons

ISBN: 9783055017698

Category: Asymptotic expansions

Page: 424

View: 5739

Asymptotic Analysis for Periodic Structures

Author: Alain Bensoussan,Jacques-Louis Lions,George Papanicolaou

Publisher: American Mathematical Soc.

ISBN: 0821853244

Category: Mathematics

Page: 392

View: 9116

This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization. In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.

Asymptotic Integration of Differential and Difference Equations

Author: Sigrun Bodine,Donald A. Lutz

Publisher: Springer

ISBN: 331918248X

Category: Mathematics

Page: 402

View: 1430

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.

Asymptotic Analysis of Solutions of Almost Diagonal Systems of Ordinary Linear Differential Equations at a Turning Point

Author: Roy Yue-Wing Lee

Publisher: N.A


Category: Differential equations, Linear

Page: 112

View: 8608

Nonlinear Partial Differential Equations

Asymptotic Behavior of Solutions and Self-Similar Solutions

Author: Mi-Ho Giga,Yoshikazu Giga,Jürgen Saal

Publisher: Springer Science & Business Media

ISBN: 9780817646516

Category: Mathematics

Page: 294

View: 1034

This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.

Applied Asymptotic Analysis

Author: Peter David Miller

Publisher: American Mathematical Soc.

ISBN: 0821840789

Category: Mathematics

Page: 467

View: 772

"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects."--BOOK JACKET.

Asymptotic Treatment of Differential Equations

Author: A. Georgescu

Publisher: CRC Press

ISBN: 9780412558603

Category: Mathematics

Page: 272

View: 1550

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.

Asymptotic Analysis of Fields in Multi-structures

Author: Vladimir Kozlov,V. G. Mazʹi͡a,Alexander B. Movchan

Publisher: Oxford University Press

ISBN: 9780198514954

Category: Mathematics

Page: 282

View: 859

The asymptotic analysis of boundary value problems in parameter-dependent domains is a rapidly developing field of research in the theory of partial differential equations, with important applications in electrostatics, elasticity, hydrodynamics and fracture mechanics. Building on the work of Ciarlet and Destuynder, this book provides a systematic coverage of these methods in multi-structures, i.e. domains which are dependent on a small parameter e in such a way that the limit region consists of subsets of different space dimensions. An undergraduate knowledge of partial differential equations and functional analysis is assumed.

Asymptotic Expansions for Ordinary Differential Equations

Author: Wolfgang Wasow

Publisher: Courier Corporation

ISBN: 9780486495187

Category: Mathematics

Page: 374

View: 5730

"A book of great value . . . it should have a profound influence upon future research."--Mathematical Reviews. Hardcover edition. The foundations of the study of asymptotic series in the theory of differential equations were laid by Poincaré in the late 19th century, but it was not until the middle of this century that it became apparent how essential asymptotic series are to understanding the solutions of ordinary differential equations. Moreover, they have come to be seen as crucial to such areas of applied mathematics as quantum mechanics, viscous flows, elasticity, electromagnetic theory, electronics, and astrophysics. In this outstanding text, the first book devoted exclusively to the subject, the author concentrates on the mathematical ideas underlying the various asymptotic methods; however, asymptotic methods for differential equations are included only if they lead to full, infinite expansions. Unabridged Dover republication of the edition published by Robert E. Krieger Publishing Company, Huntington, N.Y., 1976, a corrected, slightly enlarged reprint of the original edition published by Interscience Publishers, New York, 1965. 12 illustrations. Preface. 2 bibliographies. Appendix. Index.

Some Asymptotic Problems in the Theory of Partial Differential Equations

Author: Olga Oleinik

Publisher: Cambridge University Press

ISBN: 9780521485371

Category: Mathematics

Page: 202

View: 1498

In this book, Professor Oleinik highlights her work in the area of partial differential equations. The book is divided into two parts: the first is devoted to the study of the asymptotic behavior at infinity of solutions of a class of nonlinear second order elliptic equations in unbounded and, in particular, cylindrical domains. The second contains the most recent results of the author in the theory of homogenization of partial differential equations and is concerned with questions about partially perforated domains and of solutions with rapidly alternating types of boundary conditions. Many of the results here have not appeared in book form before, and it sheds new light on the subject, raising many new ideas and open problems.

Asymptotic Analysis

Author: J.D. Murray

Publisher: Springer Science & Business Media

ISBN: 1461211220

Category: Mathematics

Page: 165

View: 5458

From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's Asymptotic Expansions or N.G. de Bruijn's Asymptotic Methods in Analysis (1958), any academic library would do well to have this excellent introduction." (S. Puckette, University of the South) #Choice Sept. 1984#1

Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations

Author: P.L. Sachdev,Ch. Srinivasa Rao

Publisher: Springer Science & Business Media

ISBN: 0387878092

Category: Mathematics

Page: 231

View: 9568

A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.

Asymptotic Analysis for Functional Stochastic Differential Equations

Author: Jianhai Bao,George Yin,Chenggui Yuan

Publisher: Springer

ISBN: 3319469797

Category: Mathematics

Page: 151

View: 6160

This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.

Asymptotic Analysis of Singular Perturbations

Author: W. Eckhaus

Publisher: Elsevier

ISBN: 9780080875309

Category: Mathematics

Page: 286

View: 891

Asymptotic Analysis of Singular Perturbations

Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters

Author: H.G. Kaper,Marc Garbey

Publisher: Springer Science & Business Media

ISBN: 9401118108

Category: Mathematics

Page: 372

View: 2344

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.

Asymptotic Analysis and Perturbation Theory

Author: William Paulsen

Publisher: CRC Press

ISBN: 1466515120

Category: Mathematics

Page: 550

View: 6121

Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Suitable for those who have completed the standard calculus sequence, the book assumes no prior knowledge of differential equations. It explains the exact solution of only the simplest differential equations, such as first-order linear and separable equations. With varying levels of problems in each section, this self-contained text makes the difficult subject of asymptotics easy to comprehend. Along the way, it explores the properties of some important functions in applied mathematics. Although the book emphasizes problem solving, some proofs are scattered throughout to give readers a justification for the methods used.

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