ISSN:
1572-9044
Keywords:
Delay differential equation
;
parallel continuous explicit Runge-Kutta methods
;
vanishing lag
;
iterated continuous extensions
;
primary 65Q05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We present an explicit Runge-Kutta scheme devised for the numerical solution ofdelay differential equations (DDEs) where a delayed argument lies in the current Runge-Kutta interval. This can occur when the lag is small relative to the stepsize, and the more obvious extensions of the explicit Runge-Kutta method produce implicit equations. It transpires that the scheme is suitable forparallel implementation for solving both ODEs and more general DDEs. We associate our method with a Runge-Kutta tableau, from which the order of the method can be determined. Stability will affect the usefulness of the scheme and we derive the stability equations of the scheme when applied to the constant-coefficient test DDEu′(t)=λu(t) +μu(t −τ), where the lagτ and the Runge-Kutta stepsizeH n ≡H are both constant. (The caseμ=0 is treated separately.) In the case thatμ ≠ 0, we consider the two distinct possibilities: (i)τ ≥H and (ii)τ〈H.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02072017
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