A Focal Boundary Value Problem For 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 | : Stephen A. Wirkus |
Publisher | : CRC Press |
Total Pages | : 788 |
Release | : 2017-01-24 |
Genre | : Mathematics |
ISBN | : 1498736068 |
Download A Course in Differential Equations with Boundary Value Problems Book in PDF, Epub and Kindle
A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author’s successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB®, Mathematica®, and MapleTM. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. Features MATLAB®, Mathematica®, and MapleTM are incorporated at the end of each chapter All three software packages have parallel code and exercises There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a "crash course" in the three software packages Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book
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 | : Sujaul Chowdhury |
Publisher | : CRC Press |
Total Pages | : 77 |
Release | : 2021-10-25 |
Genre | : Mathematics |
ISBN | : 1000486141 |
Download Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations Book in PDF, Epub and Kindle
The book presents in comprehensive detail numerical solutions to boundary value problems of a number of non-linear differential equations. Replacing derivatives by finite difference approximations in these differential equations leads to a system of non-linear algebraic equations which we have solved using Newton’s iterative method. In each case, we have also obtained Euler solutions and ascertained that the iterations converge to Euler solutions. We find that, except for the boundary values, initial values of the 1st iteration need not be anything close to the final convergent values of the numerical solution. Programs in Mathematica 6.0 were written to obtain the numerical solutions.
Author | : Lloyd Jackson |
Publisher | : |
Total Pages | : 84 |
Release | : 1960 |
Genre | : Boundary value problems |
ISBN | : |
Download A Study of the Boundary Value Problem for Nonlinear Second Order Ordinary Differential Equations Book in PDF, Epub and Kindle
Author | : Cathryn Rudd Denny |
Publisher | : |
Total Pages | : 62 |
Release | : 1991 |
Genre | : Boundary value problems |
ISBN | : |
Download A Focal Boundary Value Problem for Difference Equations Book in PDF, Epub and Kindle
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 | : 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 | : Charles Henry Edwards |
Publisher | : Pearson |
Total Pages | : 0 |
Release | : 2015 |
Genre | : Boundary value problems |
ISBN | : 9780321796981 |
Download Differential Equations and Boundary Value Problems Book in PDF, Epub and Kindle
Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies.