Good Behavior with Respect to the Stiffness in the Numerical Integration of Retarded Functional Differential Equations

In this paper we obtain, for the global errors of a functional continuous Runge--Kutta (FCRK) method as applied to a retarded functional differential equation (RFDE), a recursive relation similar to that obtained for the global errors of a one-step method as applied to an ordinary differential equation. After which, we introduce a notion of good behavior with respect to the stiffness of an FCRK method on a given family of RFDEs. Finally, we analyze this notion of “good behavior” in the case of particular families of scalar semilinear RFDEs with nonvanishing delays.

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