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Runge-Kutta theory for Volterra integral equations of the second kind


Authors: H. Brunner, E. Hairer and S. P. Nørsett
Journal: Math. Comp. 39 (1982), 147-163
MSC: Primary 65R20
DOI: https://doi.org/10.1090/S0025-5718-1982-0658219-8
MathSciNet review: 658219
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Abstract: The present paper develops the theory of general Runge-Kutta methods for Volterra integral equations of the second kind. The order conditions are derived by using the theory of P-series, which for our problem reduces to the theory of V-series. These results are then applied to two special classes of Runge-Kutta methods introduced by Pouzet and by Beĺtyukov.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0658219-8
Keywords: Volterra integral equations of the second kind, Runge-Kutta methods, order conditions
Article copyright: © Copyright 1982 American Mathematical Society