In this paper we deal with a very general class of Runge-Kutta methods for the numerical solution of Volterra integro-differential equations. Our main contribution is the development of the theory of Natural Continuos Extensions (NCEs), i.e. piecewise polynomials functions which interpolate the values given by the Runge-Kutta methods at mesh points. The particular features of the NCEs allow to construct tail approximations which are quite efficient since they require a minimal number of kernel evaluations

Natural continuous extensions for Runge-Kutta methods for Volterra integrodifferential equations

VERMIGLIO, Rossana
1988

Abstract

In this paper we deal with a very general class of Runge-Kutta methods for the numerical solution of Volterra integro-differential equations. Our main contribution is the development of the theory of Natural Continuos Extensions (NCEs), i.e. piecewise polynomials functions which interpolate the values given by the Runge-Kutta methods at mesh points. The particular features of the NCEs allow to construct tail approximations which are quite efficient since they require a minimal number of kernel evaluations
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/671869
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