Numerical Methods for Delay Differential Equations

Overview

"The mainpurpose 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 ofter 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
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Overview

"The mainpurpose 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 ofter 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 literatire, and develps an exhaustive error and well-posedness analysis for the general classes of one-step and multistep methods."
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Editorial Reviews

From the Publisher
"...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
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Product Details

  • ISBN-13: 9780199671373
  • Publisher: Oxford University Press, USA
  • Publication date: 4/6/2013
  • Edition description: Reprint
  • Pages: 410
  • Product dimensions: 6.00 (w) x 9.10 (h) x 1.00 (d)

Meet 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

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Table of Contents

1 Introduction 1
2 Existence and regularity of solutions of DDEs 20
3 A review of DDE methods 36
4 The standard approach via continuous ODE methods 62
5 Continuous Runge - Kutta methods for ODEs 110
6 Runge - Kutta methods for DDEs 152
7 Local error estimate and variable stepsize 183
8 Stability analyses of Runge-Kutta methods for ODEs 213
9 Stability analysis of DDEs 248
10 Stability analysis of Runge-Kutta methods for DDEs 290
References 374
Index 392
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