A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations |
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Authors: | K J In 't Hout |
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Institution: | (1) Department of Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands |
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Abstract: | This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU(t)=U(t)+U(t–) with , C, Re()<–||, and >0. Ifc
i
denotes theith abscissa of a given Runge-Kutta method, then in thenth stept
n–1t
n
:=t
n–1+h of the numerical process our interpolation procedure computes an approximation toU(t
n–1+c
i
h–) from approximations that have already been generated by the process at pointst
j–1+c
i
h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem. |
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Keywords: | AMS(MOS): 65L20 CR: 5 17 |
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