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Singular Perturbations Of Boundary Value Problems For Linear Second Order Ordinary Differential Equations
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Book Synopsis Singular Perturbations of Boundary Value Problems for Linear Second-order Ordinary Differential Equations by : Tom C. Smith
Download or read book Singular Perturbations of Boundary Value Problems for Linear Second-order Ordinary Differential Equations written by Tom C. Smith and published by . This book was released on 1971 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singular Perturbations and Asymptotics by : Richard E. Meyer
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.
Book Synopsis Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos
Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
Book Synopsis The Boundary Function Method for Singular Perturbed Problems by : Adelaida B. Vasil'eva
Download or read book The Boundary Function Method for Singular Perturbed Problems written by Adelaida B. Vasil'eva and published by SIAM. This book was released on 1995-01-01 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted solely to the boundary function method, which is one of the asymptotic methods.
Book Synopsis Singularly Perturbed Differential Equations by : Herbert Goering
Download or read book Singularly Perturbed Differential Equations written by Herbert Goering and published by Walter de Gruyter GmbH & Co KG. This book was released on 1984-01-14 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Singularly Perturbed Differential Equations".
Book Synopsis Boundary Value Problems for Second Order Ordinary Differential Equations and Applications to Singular Perturbation Problems ... by : Tai-Chi Lee
Download or read book Boundary Value Problems for Second Order Ordinary Differential Equations and Applications to Singular Perturbation Problems ... written by Tai-Chi Lee and published by . This book was released on 1975 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Analysis of Singular Perturbation Problems by : P. W. Hemker
Download or read book Numerical Analysis of Singular Perturbation Problems written by P. W. Hemker and published by . This book was released on 1979 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 14 lectures by the invited speakers and 14 shorter contributions from the other speakers (pref.)
Book Synopsis Singularly Perturbed Boundary-Value Problems by : Luminita Barbu
Download or read book Singularly Perturbed Boundary-Value Problems written by Luminita Barbu and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for phenomena in biology, chemistry, and engineering. The authors are particularly interested in nonlinear problems, which have gone little-examined so far in literature dedicated to singular perturbations. The treatment presented here combines successful results from functional analysis, singular perturbation theory, partial differential equations, and evolution equations.
Book Synopsis Methods and Applications of Singular Perturbations by : Ferdinand Verhulst
Download or read book Methods and Applications of Singular Perturbations written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Book Synopsis Singular Perturbations by : Elena Shchepakina
Download or read book Singular Perturbations written by Elena Shchepakina and published by Springer. This book was released on 2014-10-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate students for the later chapters.
Book Synopsis Singularly Perturbed Differential Equations by : Herbert Goering
Download or read book Singularly Perturbed Differential Equations written by Herbert Goering and published by . This book was released on 1983 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems by : Graef John R
Download or read book Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems written by Graef John R and published by World Scientific. This book was released on 2018-09-18 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.
Book Synopsis Boundary Value Problems From Higher Order Differential Equations by : Ravi P Agarwal
Download or read book Boundary Value Problems From Higher Order Differential Equations written by Ravi P Agarwal and published by World Scientific. This book was released on 1986-07-01 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Some ExamplesLinear ProblemsGreen's FunctionMethod of Complementary FunctionsMethod of AdjointsMethod of ChasingSecond Order EquationsError Estimates in Polynomial InterpolationExistence and UniquenessPicard's and Approximate Picard's MethodQuasilinearization and Approximate QuasilinearizationBest Possible Results: Weight Function TechniqueBest Possible Results: Shooting MethodsMonotone Convergence and Further ExistenceUniqueness Implies ExistenceCompactness Condition and Generalized SolutionsUniqueness Implies UniquenessBoundary Value FunctionsTopological MethodsBest Possible Results: Control Theory MethodsMatching MethodsMaximal SolutionsMaximum PrincipleInfinite Interval ProblemsEquations with Deviating Arguments Readership: Graduate students, numerical analysts as well as researchers who are studying open problems. Keywords:Boundary Value Problems;Ordinary Differential Equations;Green's Function;Quasilinearization;Shooting Methods;Maximal Solutions;Infinite Interval Problems
Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Book Synopsis A Study of the Boundary Value Problem for Nonlinear Second Order Ordinary Differential Equations by : Lloyd Jackson
Download or read book A Study of the Boundary Value Problem for Nonlinear Second Order Ordinary Differential Equations written by Lloyd Jackson and published by . This book was released on 1960 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by : A.K. Aziz
Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.
Book Synopsis Singular Perturbations and Differential Inequalities by : Frederick A. Howes
Download or read book Singular Perturbations and Differential Inequalities written by Frederick A. Howes and published by American Mathematical Soc.. This book was released on 1976 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author discusses the singularly perturbed second-order boundary value problem [lowercase Greek]Epsilon [italic]y′′ = [italic]f([italic]t,[italic]y,[italic]y′, [lowercase Greek]Epsilon), by means of several second-order differential inequality theorems. This article not only gives a unified presentation of much of the body of results on this boundary value problem obtained in the last twenty years or so, but contains very considerable improvements involving less demanding conditions (sometimes leading to weaker results) in some cases, more precise results (sometimes under more severe restrictions) in other cases, and a more thorough investigation of the general boundary conditions. Some potential extensions to transition point problems and the like are indicated (but not carried out in detail) in the last section.
