Abstract
In this paper we analyze the attainable order ofm-stage implicit (collocation-based) Runge-Kutta methods for differential equations and Volterra integral equations of the second kind with variable delay of the formqt (0<q<1). It will be shown that, in contrast to equations without delay, or equations with constant delay, collocation at the Gauss (-Legendre) points will no longer yield the optimal (local) orderO(h 2m).
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This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Research Grant OGP0009406).
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Brunner, H. On the discretization of differential and Volterra integral equations with variable delay. Bit Numer Math 37, 1–12 (1997). https://doi.org/10.1007/BF02510168
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DOI: https://doi.org/10.1007/BF02510168