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.

Good behaviour with respect to the stiffness in the numerical integration of retarded functional differential equations

MASET, STEFANO;ZENNARO, MARINO
2014-01-01

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2805928
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