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| Author | : Bailey |
| Publisher | : Academic Press |
| Total Pages | : 190 |
| Release | : 1968 |
| Genre | : Computers |
| ISBN | : 0080955525 |
Nonlinear Two Point Boundary Value Problems
| Author | : Herbert B. Keller |
| Publisher | : SIAM |
| Total Pages | : 69 |
| Release | : 1976-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970449 |
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 | : C. De Coster |
| Publisher | : Elsevier |
| Total Pages | : 502 |
| Release | : 2006-03-21 |
| Genre | : 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 | : Herbert B. Keller |
| Publisher | : Courier Dover Publications |
| Total Pages | : 417 |
| Release | : 2018-11-14 |
| Genre | : Mathematics |
| ISBN | : 0486828344 |
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 | : Milan Kubicek |
| Publisher | : Courier Corporation |
| Total Pages | : 338 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486463001 |
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 | : Paul W. Eloe |
| Publisher | : World Scientific |
| Total Pages | : 249 |
| Release | : 2016 |
| Genre | : Mathematics |
| ISBN | : 9814733482 |
"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 | : Milton Lees |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 1960 |
| Genre | : Boundary value problems |
| ISBN | : |
| Author | : Lakshmikantham |
| Publisher | : Academic Press |
| Total Pages | : 385 |
| Release | : 1974-05-31 |
| Genre | : Computers |
| ISBN | : 0080956181 |
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 | : |
| Total Pages | : 232 |
| Release | : 1965 |
| Genre | : Boundary value problems |
| ISBN | : |
| Author | : Wen Shen |
| Publisher | : World Scientific |
| Total Pages | : 339 |
| Release | : 2019-08-28 |
| Genre | : Mathematics |
| ISBN | : 9811204438 |
This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.The book covers many of the introductory topics for a first course in numerical computation, which fits in the short time frame of a semester course. Topics range from polynomial approximations and interpolation, to numerical methods for ODEs and PDEs. Emphasis was made more on algorithm development, basic mathematical ideas behind the algorithms, and the implementation in Matlab.The book is supplemented by two sets of videos, available through the author's YouTube channel. Homework problem sets are provided for each chapter, and complete answer sets are available for instructors upon request.The second edition contains a set of selected advanced topics, written in a self-contained manner, suitable for self-learning or as additional material for an honored version of the course. Videos are also available for these added topics.
