Numerical Methods for Delay Differential Equations

Autor: Alfredo Bellen, Marino Zennaro

Język:

Oprawa: Miękka

Wydawca: Oxford University Press

Dostępność: 50 % szansa

Przeszukamy cały świat

436.73 zł

The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy...

Informacje o książce

Autor

Alfredo Bellen, Marino Zennaro

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2013

strony

410

EAN

9780199671373

ISBN

0199671370

Enbook ID

04867258

Wydawca

Oxford University Press

Waga

626

Wymiary

288 x 242 x 36

Pełny opis

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.

Możesz być zainteresowany

Klienci, którzy kupili tę książkę, kupili również

Najczęściej wyszukiwane

Categories

Authors

Publishers

Produkty

Produkty

Najczęściej wyszukiwane

Categories

Authors

Publishers

Produkty

Produkty

Numerical Methods for Delay Differential Equations

Informacje o książce

Pełny opis

Możesz być zainteresowany

Klienci, którzy kupili tę książkę, kupili również