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NUMERICAL METHODS FOR DELAY DIFFERENTIAL EQUATIONS By Alfredo Bellen & Marino
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N.º de artículo de eBay:375541376226
Características del artículo
- Estado
- En buen estado
- Notas del vendedor
- “Cover/edge wear. Highlighting in yellow. Good otherwise. See photos.”
- ISBN-10
- 0198506546
- Book Title
- Numerical Methods for Delay Differential Equations (Numerical
- ISBN
- 9780198506546
Acerca de este producto
Product Identifiers
Publisher
Oxford University Press, Incorporated
ISBN-10
0198506546
ISBN-13
9780198506546
eBay Product ID (ePID)
2306760
Product Key Features
Number of Pages
410 Pages
Language
English
Publication Name
Numerical Methods for Delay Differential Equations
Publication Year
2003
Subject
Differential Equations / General
Type
Textbook
Subject Area
Mathematics
Series
Numerical Mathematics and Scientific Computation Ser.
Format
Hardcover
Dimensions
Item Height
1 in
Item Weight
24.7 Oz
Item Length
9.2 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2003-271859
Reviews
"...this is a serious monograph...It will serve as a guide and a reference for researchers and engineers interested in numerical solution of models from real-life applications. It may also serve as a textbook for a graduate-level course in this area that may be offered at some universities."-- SIAM Review, "...this is a serious monograph...It will serve as a guide and a reference for researchers and engineers interested in numerical solution of models from real-life applications. It may also serve as a textbook for a graduate-level course in this area that may be offered at some universities."--SIAMReview, "...this is a serious monograph...It will serve as a guide and a reference for researchers and engineers interested in numerical solution of models from real-life applications. It may also serve as a textbook for a graduate-level course in this area that may be offered at some universities."--SIAM Review
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
515/.35
Table Of Content
1. Introduction2. Existence and regularity of solutions of DDEs3. A review of DDE methods4. The standard approach via continuous ODE methods5. Continuous Runge-Kutta methods for ODEs6. Runge-Kutta methods for DDEs7. Local error estimation and variable stepsize8. Stability analysis of Runge-Kutta methods for ODEs9. Stability analysis of DDEs10. Stability analysis of Runge-Kutta methods for DDEs
Synopsis
This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own., The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that DDEs exhibit with respect to ordinary differential equations are preliminarily outlined by numerous examples illustrating some unexpected, and often surprising behaviors of the analytical and numerical solutions. The effect of various kinds of delays on the regularity of the solution is described and some essential existence and uniqueness results are reported. The book is centered on the various approaches existing in the literature, and develops an exhaustive error and well-posedness analysis for the general classes of one-step and multistep methods., The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that DDEs exhibit with respect to ordinary differential equations are preliminarily outlined by numerous examples illustrating some unexpected, and often surprising, behaviours of the analytical and numerical solutions. The effect of various kinds of delays on the regularity of the solution is described and some essential existence and uniqueness results are reported. The book is centered on the use of Runge-Kutta methods continuously extended by polynomial interpolation, includes a brief review of the various approaches existing in the literature, and develops an exhaustive error and well-posedness analysis for the general classes of one-step and multistep methods. The book presents a comprehensive development of continuous extensions of Runge-Kutta methods which are of interest also in the numerical treatment of more general problems such as dense output, discontinuous equations, etc. Some deeper insight into convergence and superconvergence of continuous Runge-Kutta methods is carried out for DDEs with various kinds of delays. The stepsize control mechanism is also developed on a firm mathematical basis relying on the discrete and continuous local error estimates. Classical results and a unconventional analysis of "stability with respect to forcing term" is reviewed for ordinary differential equations in view of the subsequent numerical stability analysis. Moreover, an exhaustive description of stability domains for some test DDEs is carried out and the corresponding stability requirements for the numerical methods are assessed and investigated. Alternative approaches, based on suitable formulation of DDEs as partial differential equations and subsequent semidiscretization are briefly described and compared with the classical approach. A list of available codes is provided, and illustrative examples, pseudo-codes and numerical experiments are included throughout the book.Series Editors: G. H. Golub (Stanford University)C. Schwab (ETH Zurich)W. A. Light (University of Leicester)E. Süli (University of Oxford)Recent developments in the field of numerical analysis have radically changed the nature of the subject. Firstly, the increasing power and availability of computer workstations has allowed the widespread feasibility of complex numerical computations, and the demands of mathematical modelling are expanding at a corresponding rate. In addition to this, the mathematical theory of numerical mathematics itself is growing in sophistication, and numerical analysis now generates research into relatively abstract mathematics.Oxford University Press has had an established series Monographs in Numerical Analysis, including Wilkinson's celebrated treatise The Algebraic Eigenvalue Problem. In the face of the developments in the field this has been relaunched as the Numerical Mathematics and Scientific Computation series. As its name suggests, the series will now aim to cover the broad subject area concerned with theoretical and computational aspects of modern numerical mathematics., The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that DDEs exhibit with respect to ordinary differential equations are preliminarily outlined by numerous examples illustrating some unexpected, and often surprising, behaviours of the analytical and numerical solutions. The effect of various kinds of delays on the regularity of the solution is described and some essential existence and uniqueness results are reported. The book is centered on the use of Runge-Kutta methods continuously extended by polynomial interpolation, includes a brief review of the various approaches existing in the literature, and develops an exhaustive error and well-posedness analysis for the general classes of one-step and multistep methods. The book presents a comprehensive development of continuous extensions of Runge-Kutta methods which are of interest also in the numerical treatment of more general problems such as dense output, discontinuous equations, etc. Some deeper insight into convergence and superconvergence of continuous Runge-Kutta methods is carried out for DDEs with various kinds of delays. The stepsize control mechanism is also developed on a firm mathematical basis relying on the discrete and continuous local error estimates. Classical results and a unconventional analysis of "stability with respect to forcing term" is reviewed for ordinary differential equations in view of the subsequent numerical stability analysis. Moreover, an exhaustive description of stability domains for some test DDEs is carried out and the corresponding stability requirements for the numerical methods are assessed and investigated. Alternative approaches, based on suitable formulation of DEs as partial differential equations and subsequent semidiscretization are briefly described and compared with the classical approach. A list of available codes is provided, and illustrative examples, pseudo-codes and numerical experiments are included throughout the book.Series Editors: G. H. Golub (Stanford University)C. Schwab (ETH Zurich)W. A. Light (University of Leicester)E. Süli (University of Oxford)Recent developments in the field of numerical analysis have radically changed the nature of the subject. Firstly, the increasing power and availability of computer workstations has allowed the widespread feasibility of complex numerical computations, and the demands of mathematical modelling are expanding at a corresponding rate. In addition to this, the mathematical theory of numerical mathematics itself is growing in sophistication, and numerical analysis now generates research into relatively abstract mathematics.Oxford University Press has had an established series Monographs in Numerical Analysis, including Wilkinson's celebrated treatise The Algebraic Eigenvalue Problem. In the face of the developments in the field this has been relaunched as the Numerical Mathematics and Scientific Computation series. As its name suggests, the series will now aim to cover the broad subject area concerned with theoretical and computational aspects of modern numerical mathematics.
LC Classification Number
QA371
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