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Runge-Kutta Theory for Volterra Integral Equations of the Second Kind

H. Brunner, E. Hairer and S. P. Nørsett
Mathematics of Computation
Vol. 39, No. 159 (Jul., 1982), pp. 147-163
DOI: 10.2307/2007625
Stable URL: http://www.jstor.org/stable/2007625
Page Count: 17
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Runge-Kutta Theory for Volterra Integral Equations of the Second Kind
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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 Beltyukov.

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