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Numerical Methods for Delay Differential Equations
Alfredo Bellen and Marino Zennaro
Numerical Methods for Delay Differential Equations
ean9780199671373
temáticaMATEMÁTICAS
año Publicación2013
idiomaINGLÉS
editorialOXFORD UNIVERSITY PRESS
formatoCARTONÉ


42,34 €


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matemáticas
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.

Readership : The text is intended for a large variety of readers including mathematicians, physicists, engineers, economists and other scientists ranging from specialists in numerical analysis of differential equations to any researcher interested in simulating phenomena modeled by differential equations with lag terms.

indíce
1. Introduction
2. Existence and regularity of solutions of DDEs
3. A review of DDE methods
4. The standard approach via continuous ODE methods
5. Continuous Runge-Kutta methods for ODEs
6. Runge-Kutta methods for DDEs
7. Local error estimation and variable stepsize
8. Stability analysis of Runge-Kutta methods for ODEs
9. Stability analysis of DDEs
10. Stability analysis of Runge-Kutta methods for DDEs
There are no Instructor/Student Resources available at this time.
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, Università di Trieste, Italy.

Making Sense - Margot Northey and Joan McKibbin
Numerical Methods for Delay Differential Equations - Alfredo Bellen and Marino Zennaro
Numerical Analysis and Optimization - Grégoire Allaire
Alan Craig

Special Features

Comprehensive treatment of covergence, error estimation, stepsize control and stability in the numerical solution of delay differential equations.Exhaustive description and self-contained analysis of continuous Runge-Kutta methods.Numerous illustrative examples and assistance with codes.Many plots and tables of numerical experiments.Exhaustive list of references to existing software with a synthetic description of each code.






Finançat per UE