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Author : Bailey
Publisher : Academic Press
Page : 190 pages
File Size : 50,6 Mb
Release : 1968
Category : Computers
ISBN : 9780080955520
Nonlinear Two Point Boundary Value Problems
Author : Herbert B. Keller
Publisher : SIAM
Page : 69 pages
File Size : 51,6 Mb
Release : 1976-01-01
Category : Mathematics
ISBN : 161197044X
Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
Author : Herbert B. Keller
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 53,6 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9780486828343
Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.
Author : Paul W. Eloe,Johnny Henderson
Publisher : World Scientific
Page : 249 pages
File Size : 51,9 Mb
Release : 2016
Category : Mathematics
ISBN : 9789814733489
"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 : Milan Kubicek,Vladimir Hlavacek
Publisher : Courier Corporation
Page : 338 pages
File Size : 52,7 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486463001
A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.
Author : Milton Lees
Publisher : Unknown
Page : 30 pages
File Size : 50,7 Mb
Release : 1960
Category : Boundary value problems
ISBN : UOM:39015095242452
Author : C. De Coster,P. Habets
Publisher : Elsevier
Page : 502 pages
File Size : 48,7 Mb
Release : 2006-03-21
Category : Mathematics
ISBN : 0080462472
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
Author : Sanford M. Roberts,Jerome S. Shipman
Publisher : Elsevier Publishing Company
Page : 300 pages
File Size : 53,5 Mb
Release : 1972
Category : Mathematics
ISBN : UOM:39015013040491
Author : Lakshmikantham
Publisher : Academic Press
Page : 385 pages
File Size : 41,9 Mb
Release : 1974-05-31
Category : Computers
ISBN : 9780080956183
A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.
Author : Richard Bellman
Publisher : Unknown
Page : 232 pages
File Size : 48,8 Mb
Release : 1965
Category : Boundary value problems
ISBN : STANFORD:36105033284410
Author : Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell
Publisher : SIAM
Page : 620 pages
File Size : 48,8 Mb
Release : 1994-12-01
Category : Mathematics
ISBN : 1611971233
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 : Jay M. Lewallen
Publisher : Unknown
Page : 28 pages
File Size : 47,5 Mb
Release : 1967
Category : Nonlinear boundary value problems
ISBN : UIUC:30112106870352
Author : Renate Schaaf
Publisher : Springer
Page : 160 pages
File Size : 43,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540467427
The book deals with parameter dependent problems of the form u"+*f(u)=0 on an interval with homogeneous Dirichlet or Neuman boundary conditions. These problems have a family of solution curves in the (u,*)-space. By examining the so-called time maps of the problem the shape of these curves is obtained which in turn leads to information about the number of solutions, the dimension of their unstable manifolds (regarded as stationary solutions of the corresponding parabolic prob- lem) as well as possible orbit connections between them. The methods used also yield results for the period map of certain Hamiltonian systems in the plane. The book will be of interest to researchers working in ordinary differential equations, partial differential equations and various fields of applications. By virtue of the elementary nature of the analytical tools used it can also be used as a text for undergraduate and graduate students with a good background in the theory of ordinary differential equations.
Author : Herbert B. Keller
Publisher : Courier Dover Publications
Page : 416 pages
File Size : 40,5 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9780486835624
Elementary yet rigorous, this concise treatment explores practical numerical methods for solving very general two-point boundary-value problems. The approach is directed toward students with a knowledge of advanced calculus and basic numerical analysis as well as some background in ordinary differential equations and linear algebra. After an introductory chapter that covers some of the basic prerequisites, the text studies three techniques in detail: initial value or "shooting" methods, finite difference methods, and integral equations methods. Sturm-Liouville eigenvalue problems are treated with all three techniques, and shooting is applied to generalized or nonlinear eigenvalue problems. Several other areas of numerical analysis are introduced throughout the study. The treatment concludes with more than 100 problems that augment and clarify the text, and several research papers appear in the Appendixes.
Author : Leszek Gasinski,Nikolaos S. Papageorgiou
Publisher : CRC Press
Page : 792 pages
File Size : 47,7 Mb
Release : 2004-07-27
Category : Mathematics
ISBN : 9781420035032
Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances. This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature. Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of problems.