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Natural continuous extension of Runge-Kutta methods for Volterra integrodiffential equations. (English) Zbl 0629.65145

We deal with a very general class of Runge-Kutta (RK) methods for numerical solution of Volterra integrodifferential equations. Our main contribution is the development of the theory of natural continuous extensions (NCEs), i.e. piecewise polynomial functions which interpolate the values given by the RK-method at the mesh points. The particular features of these NCEs allow us to construct tail approximations which are quite efficient since they require a minimal number of kernel evaluations.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
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References:

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