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Numerical Methods for Delay Differential Equations by Alfredo Bellen, Marino Zennaro (Paperback, 2013)

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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 polymial 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.

Product Identifiers

Publisher
Oxford University Press
ISBN-10
0199671370
ISBN-13
9780199671373
eBay Product ID (ePID)
138799552

Product Key Features

Author
Alfredo Bellen, Marino Zennaro
Format
Paperback
Language
English
Subject
Mathematics
Type
Textbook

Dimensions

Weight
622g
Height
232mm
Width
156mm

Additional Product Features

Place of Publication
Oxford
Spine
22mm
Series Title
Numerical Mathematics & Scientific Computation
Content Note
60 B/w Line Drawings
Author Biography
Alfredo Bellen is Professor of Numerical Calculus in the Dipartimento di Matematica e Informatica, Universita' di Trieste, Italy Marino Zennaro is Professor of Numerical Analysis in the Dipartimento di Matematica e Geoscienze, Universita di Trieste, Italy
Date of Publication
10/01/2013
Country of Publication
United Kingdom
Genre
Mathematics

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Numerical Methods for Delay Differential Equations by Alfredo Bellen, Marino Zennaro (Paperback, 2013)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

Best Selling in Adult Learning & University

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Save on Adult Learning & University

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