Numerical Methods for Delay Differential Equations by Alfredo Bellen

Numerical Methods for Delay Differential Equations

byAlfredo Bellen, Marino Zennaro

Paperback | January 10, 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 examplesillustrating 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 ofRunge-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 continuousRunge-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 forcingterm" 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 andinvestigated. 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 experimentsare included throughout the book.

About The Author

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.
Numerical Methods for Delay Differential Equations
Numerical Methods for Delay Differential Equations

by Alfredo Bellen


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Details & Specs

Title:Numerical Methods for Delay Differential EquationsFormat:PaperbackDimensions:410 pages, 9.21 × 6.14 × 0.01 inPublished:January 10, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199671370

ISBN - 13:9780199671373

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Extra Content

Table of Contents

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

Editorial Reviews

Review from previous edition: "I believe the book will become a standard reference." --Mathematical Reviews 05/08/2004