Abstract
The interest in the concept of “effective order” has been revived by its rediscovery in applications to symplectic problems. In this paper we revert to the original application, the construction of explicit Runge–Kutta methods. Changing stepsize is a characteristic difficulty with effective order methods and we propose a way of overcoming this difficulty. We also consider the possible cancellation of local truncation errors of two methods over two successive steps. Using the algebraic approach for deriving these results gives us further insight into these methods and compositions of methods. A particular sixth stage Runge–Kutta pair is derived in the paper and is shown to be competitive.
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Butcher, J., Chan, T. Variable stepsize schemes for effective order methods and enhanced order composition methods. Numerical Algorithms 26, 131–150 (2001). https://doi.org/10.1023/A:1016628315914
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DOI: https://doi.org/10.1023/A:1016628315914