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Runge-Kutta theory for Volterra integrodifferential equations

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The present paper develops the theory of general Runge-Kutta methods for Volterra integrodifferential equations. The local order is characterized in terms of the coefficients of the method. We investigate the global convergence of mixed and extended Runge-Kutta methods and give results on asymptotic error expansions. In a further section we construct examples of methods up to order 4.

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  1. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293, D-6900, Heidelberg, Germany

    Ch. Lubich

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  1. Ch. Lubich
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Lubich, C. Runge-Kutta theory for Volterra integrodifferential equations. Numer. Math. 40, 119–135 (1982). https://doi.org/10.1007/BF01459081

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