✦ LIBER ✦

Dissipativity of multistep runge-kutta methods for dynamical systems with delays

✍ Scribed by Chengming Huang; Qianshun Chang

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 648 KB
Volume: 40
Category: Article
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2005.01.019

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✦ Synopsis

This paper is concerned with the numerical solution of dissipative initial value problems with delays by multistep Runge-Kutta methods. We investigate the dissipativity properties of (k, /)-algebraically stable multistep Runge-Kutta methods with constrained grid and linear interpolation procedure. In particular, it is proved that an algebraically stable, irreducible multistep Runge-Kutta method is dissipative for finite-dimensional dynamical systems with delays, which extends and unifies some extant results. In addition~ we obtain dissipativity results of A-stable linear multistep methods by using the relationship between one-leg methods and linear multistep methods.

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