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Stability of IMEX Runge–Kutta methods for delay differential equations

✍ Scribed by Toshiyuki Koto

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
353 KB
Volume
211
Category
Article
ISSN
0377-0427

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✦ Synopsis

Stability of IMEX (implicit-explicit) Runge-Kutta methods applied to delay differential equations (DDEs) is studied on the basis of the scalar test equation du/dt = u(t) + u(t -), where is a constant delay and , are complex parameters. More specifically, P-stability regions of the methods are defined and analyzed in the same way as in the case of the standard Runge-Kutta methods. A new IMEX method which possesses a superior stability property for DDEs is proposed. Some numerical examples which confirm the results of our analysis are presented.

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