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Book Boundary Value Problems For Functional Differential Equations

Download or read book Boundary Value Problems For Functional Differential Equations written by Johnny L Henderson and published by World Scientific. This book was released on 1995-10-12 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional differential equations have received attention since the 1920's. Within that development, boundary value problems have played a prominent role in both the theory and applications dating back to the 1960's. This book attempts to present some of the more recent developments from a cross-section of views on boundary value problems for functional differential equations.Contributions represent not only a flavor of classical results involving, for example, linear methods and oscillation-nonoscillation techiques, but also modern nonlinear methods for problems involving stability and control as well as cone theoretic, degree theoretic, and topological transversality strategies. A balance with applications is provided through a number of papers dealing with a pendulum with dry friction, heat conduction in a thin stretched resistance wire, problems involving singularities, impulsive systems, traveling waves, climate modeling, and economic control.With the importance of boundary value problems for functional differential equations in applications, it is not surprising that as new applications arise, modifications are required for even the definitions of the basic equations. This is the case for some of the papers contributed by the Perm seminar participants. Also, some contributions are devoted to delay Fredholm integral equations, while a few papers deal with what might be termed as boundary value problems for delay-difference equations.

Book Boundary Value Problems From Higher Order Differential Equations

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 Initial Boundary Value Problems and the Navier Stokes Equation

Download or read book Initial Boundary Value Problems and the Navier Stokes Equation written by Heinz-Otto Kreiss and published by SIAM. This book was released on 2004-01-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.

Book Boundary Value Problems for Systems of Differential Difference and Fractional Equations

Download or read book Boundary Value Problems for Systems of Differential Difference and Fractional Equations written by Johnny Henderson and published by Academic Press. This book was released on 2015-10-30 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. - Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions - Discusses second order difference equations with multi-point boundary conditions - Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions

Book Two Point Boundary Value Problems Lower and Upper Solutions

Download or read book Two Point Boundary Value Problems Lower and Upper Solutions written by C. De Coster and published by Elsevier. This book was released on 2006-03-21 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.· Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes

Book Oscillation Theory for Functional Differential Equations

Download or read book Oscillation Theory for Functional Differential Equations written by Lynn Erbe and published by Routledge. This book was released on 2017-10-02 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.

Book Boundary Value Problems Integral Equations And Related Problems Proceedings Of The International Conference

Download or read book Boundary Value Problems Integral Equations And Related Problems Proceedings Of The International Conference written by Guo Chun Wen and published by World Scientific. This book was released on 2000-02-22 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this proceedings volume, the following topics are discussed: (1) various boundary value problems for partial differential equations and functional equations, including free and moving boundary problems; (2) the theory and methods of integral equations and integral operators, including singular integral equations; (3) applications of boundary value problems and integral equations to mechanics and physics; (4) numerical methods of integral equations and boundary value problems; and (5) some problems related with analysis and the foregoing subjects.

Book Boundary Value Problems

Download or read book Boundary Value Problems written by Chi Yeung Lo and published by World Scientific. This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been designed for a one-year graduate course on boundary value problems for students of mathematics, engineering, and the physical sciences. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation. The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions and to verify that the formal solution possesses all the required properties. To provide the mathematical justification for this approach, the theory of Sturm-Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations.

Book The Boundary Function Method for Singular Perturbed Problems

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 Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations

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 Analysis of Finite Difference Schemes

Download or read book Analysis of Finite Difference Schemes written by Boško S. Jovanović and published by Springer Science & Business Media. This book was released on 2013-10-22 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.

Book Hyperbolic Boundary Value Problems

Download or read book Hyperbolic Boundary Value Problems written by Reiko Sakamoto and published by CUP Archive. This book was released on 1982-07-08 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary value problems are of central importance and interest not only to mathematicians but also to physicists and engineers who need to solve differential equations which govern the behaviour of physical systems. In this book, Professor Sakamoto introduces the general theory of the existence and uniqueness of solutions to the wave equation. The reader is assumed to have some familiarity with Lebesgue integration and complex function theory but other than that the book is essentially self-contained. It is therefore suited to senior undergraduates and graduates in mathematics and the mathematical sciences but can be read with profit by professionals in those subjects.

Book Boundary Value Problems and Partial Differential Equations

Download or read book Boundary Value Problems and Partial Differential Equations written by Mayer Humi and published by Brooks/Cole. This book was released on 1992 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of 15 years of teaching experience in a course on boundary value problems. It is intended to introduce junior and senior students to boundary value problems, with special emphasis on the modeling process that leads to partial differential equations.