Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems
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Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1988-01-01
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
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.
Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems
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Author : John R Graef
language : en
Publisher: World Scientific
Release Date : 2018-09-18
Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems written by John R Graef and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-18 with Mathematics categories.
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.
Two Point Boundary Value Problems
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Author : Colette De Coster
language : en
Publisher: Elsevier Science Limited
Release Date : 2006
Two Point Boundary Value Problems written by Colette De Coster and has been published by Elsevier Science Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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. Key features: - Presentation of the fundamental features of the method - Actual construction of lower and upper solutions in problems - Working applications - Illustrate theorems by examples - Description of the history of the method - Bibliographical notes Key features: - Presentation of the fundamental features of the method - Actual construction of lower and upper solutions in problems - Working applications - Illustrate theorems by examples - Description of the history of the method - Bibliographical notes
Elementary Differential Equations And Boundary Value Problems
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Author : William E. Boyce
language : en
Publisher: John Wiley & Sons
Release Date : 2017-08-21
Elementary Differential Equations And Boundary Value Problems written by William E. Boyce and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-21 with Mathematics categories.
Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
Ordinary And Partial Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-13
Ordinary And Partial Differential Equations written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-13 with Mathematics categories.
In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
Focal Boundary Value Problems For Differential And Difference Equations
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Author : R.P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Focal Boundary Value Problems For Differential And Difference Equations written by R.P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Elementary Differential Equations With Boundary Value Problems
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Author : William F. Trench
language : en
Publisher: Thomson Brooks/Cole
Release Date : 2001
Elementary Differential Equations With Boundary Value Problems written by William F. Trench and has been published by Thomson Brooks/Cole this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
Differential Equations And Boundary Value Problems
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Author : C. Henry Edwards
language : en
Publisher:
Release Date : 2022
Differential Equations And Boundary Value Problems written by C. Henry Edwards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematics categories.
"This is a textbook for the standard introductory differential equations course taken by science and engineering students. Its updated content reflects the wide availability of technical computing environments like Maple, Mathematica, and MATLAB that now are used extensively by practicing engineers and scientists. The traditional manual and symbolic methods are augmented with coverage also of qualitative and computer-based methods that employ numerical computation and graphical visualization to develop greater conceptual understanding. A bonus of this more comprehensive approach is accessibility to a wider range of more realistic applications of differential equations"--
Numerical Methods For Two Point Boundary Value Problems
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Author : Herbert Bishop Keller
language : en
Publisher:
Release Date : 1992
Numerical Methods For Two Point Boundary Value Problems written by Herbert Bishop Keller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
A brief, elementary yet rigorous account of practical numerical methods for solving very general two-point boundary-value problems. Advanced undergraduate level. Over 100 problems.