Abstract
In the numerical solution of delay differential equations by a continuous explicit Runge-Kutta method a difficulty arises when the delay vanishes or becomes smaller than the stepsize the method would like to use. In this situation the standard explicit sequential process of computing the Runge-Kutta stages becomes an implicit process and an iteration scheme must be adopted. We will consider alternative iteration schemes and investigate their order.
Zusammenfassung
Beim numerischen Lösen von Differentialgleichungen mit nacheilendem Argument (DDEs) mit Hilfe von stetigen expliziten Runge-Kutta Methoden entstehen Schwierigkeiten, wenn die Argumentverzögerung verschwindet oder zumindest kleiner als die Verfahrensschrittweite wird. In dieser Situation wird der herkömmlich explizite und sequentielle Prozeß der Stufenberechnungen des RK-Schemas ein impliziter und muß überdies iteriert werden. In dieser Arbeit werden einige Iterationsmethoden untersucht und deren Ordnung bestimmt.
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This work was supported by Natural Science and Engineering Research Council of Canada and the Information Technology Research Center of Ontario.
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Enright, W.H., Hu, M. Interpolating Runge-Kutta methods for vanishing delay differential equations. Computing 55, 223–236 (1995). https://doi.org/10.1007/BF02238433
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DOI: https://doi.org/10.1007/BF02238433