Focal Boundary Value Problems For Differential And Difference Equations
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Author | : R.P. Agarwal |
Publisher | : Springer Science & Business Media |
Total Pages | : 302 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401715688 |
Download Focal Boundary Value Problems for Differential and Difference Equations Book in PDF, Epub and Kindle
The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations. In this vast field of research, the conjugate (Hermite) and the right focal point (Abei) types of problems have received the maximum attention. This is largely due to the fact that these types of problems are basic, in the sense that the methods employed in their study are easily extendable to other types of prob lems. Moreover, the conjugate and the right focal point types of boundary value problems occur frequently in real world problems. In the monograph Boundary Value Problems for Higher Order Differential Equations published in 1986, we addressed the theory of conjugate boundary value problems. At that time the results on right focal point problems were scarce; however, in the last ten years extensive research has been done. In Chapter 1 of the mono graph we offer up-to-date information of this newly developed theory of right focal point boundary value problems. Until twenty years ago Difference Equations were considered as the dis cretizations of the differential equations. Further, it was tacitly taken for granted that the theories of difference and differential equations are parallel. However, striking diversities and wide applications reported in the last two decades have made difference equations one of the major areas of research.
Author | : Johnny Henderson |
Publisher | : Academic Press |
Total Pages | : 323 |
Release | : 2015-10-30 |
Genre | : Mathematics |
ISBN | : 0128036796 |
Download Boundary Value Problems for Systems of Differential, Difference and Fractional Equations Book in PDF, Epub and Kindle
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
Author | : Paul W. Eloe |
Publisher | : World Scientific |
Total Pages | : 249 |
Release | : 2016 |
Genre | : Mathematics |
ISBN | : 9814733482 |
Download Nonlinear Interpolation and Boundary Value Problems Book in PDF, Epub and Kindle
"This book is devoted to the study of solutions of nonlinear ODE boundary value problems as nonlinear interpolation problems. In 1967, Lasota and Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two distinct points are unique, when they exist, then, in fact, a solution passing through two distinct points does exist. That result, coupled with the pioneering work of Philip Hartman on what was then called unrestricted n-parameter families has stimulated 50 years of rapid development in the study of solutions of boundary value problems as nonlinear interpolation problems. The purpose of this book is two-fold. First, the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well-defined area of study in the qualitative theory of ordinary differential equations. Second, methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation"--
Author | : Ravi P Agarwal |
Publisher | : World Scientific |
Total Pages | : 321 |
Release | : 1986-07-01 |
Genre | : Mathematics |
ISBN | : 9814513636 |
Download Boundary Value Problems From Higher Order Differential Equations Book in PDF, Epub and Kindle
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
Author | : L Brugnano |
Publisher | : CRC Press |
Total Pages | : 438 |
Release | : 1998-05-22 |
Genre | : Mathematics |
ISBN | : 9789056991074 |
Download Solving Differential Equations by Multistep Initial and Boundary Value Methods Book in PDF, Epub and Kindle
The numerical approximation of solutions of differential equations has been, and continues to be, one of the principal concerns of numerical analysis and is an active area of research. The new generation of parallel computers have provoked a reconsideration of numerical methods. This book aims to generalize classical multistep methods for both initial and boundary value problems; to present a self-contained theory which embraces and generalizes the classical Dahlquist theory; to treat nonclassical problems, such as Hamiltonian problems and the mesh selection; and to select appropriate methods for a general purpose software capable of solving a wide range of problems efficiently, even on parallel computers.
Author | : Uri M. Ascher |
Publisher | : SIAM |
Total Pages | : 620 |
Release | : 1994-12-01 |
Genre | : Mathematics |
ISBN | : 9781611971231 |
Download Numerical Solution of Boundary Value Problems for Ordinary Differential Equations Book in PDF, Epub and Kindle
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.
Author | : Johnny Henderson |
Publisher | : |
Total Pages | : 156 |
Release | : 1981 |
Genre | : |
ISBN | : |
Download Right Focal Boundary Value Problems for Ordinary Differential Equations Book in PDF, Epub and Kindle
Author | : Graef John R |
Publisher | : World Scientific |
Total Pages | : 344 |
Release | : 2018-09-18 |
Genre | : Mathematics |
ISBN | : 9813274042 |
Download Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems Book in PDF, Epub and Kindle
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.
Author | : A.K. Aziz |
Publisher | : Academic Press |
Total Pages | : 380 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483267997 |
Download Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations Book in PDF, Epub and Kindle
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.
Author | : John R Graef |
Publisher | : World Scientific |
Total Pages | : 290 |
Release | : 2015-08-26 |
Genre | : Mathematics |
ISBN | : 9814696560 |
Download Multiple Solutions Of Boundary Value Problems: A Variational Approach Book in PDF, Epub and Kindle
Variational methods and their generalizations have been verified to be useful tools in proving the existence of solutions to a variety of boundary value problems for ordinary, impulsive, and partial differential equations as well as for difference equations. In this monograph, we look at how variational methods can be used in all these settings. In our first chapter, we gather the basic notions and fundamental theorems that will be applied in the remainder of this monograph. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with the Sturm-Liouville problems, multi-point boundary value problems, problems with impulses, partial differential equations, and difference equations. An extensive bibliography is also included.