The Approximate Runge-Kutta Computational Process |
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Authors: | Hans Olsson Gustaf Sderlind |
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Institution: | (1) Dynasim AB, Research Park Ideon, SE-223 70 Lund, Sweden;(2) Numerical Analysis, Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden. |
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Abstract: | Implicit Runge-Kutta methods are efficient for solving stiff ODEs and DAEs. To bridge the gap between their theoretical analysis and practical implementation, we introduce the notion of the (, K)-approximate Runge- Kutta process to account for inevitable iteration errors. We prove iteration error bounds uniform with respect to stiffness, and investigate stage derivative reuse for methods having a first explicit stage. The latter technique may result in significant performance gains, also when such methods are used as error estimators. Previous computational heuristics can therefore be replaced by a consistent approach supported by theoretical analysis. The approximate but well-defined computational process is evaluated using approved test problems. |
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Keywords: | Runge-Kutta computational process stage derivative reuse error bound |
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