Abstract
We propose a new rule of thumb for designing high-order composition methods for ODEs: instead of minimizing (some norm of) the principal error coefficients, simply set all the outer stages equal. This rule automatically produces families of minimum error 4th order and corrected 6th order methods, and very good standard 6th order methods, parameterized by the number of stages. Intriguingly, the most accurate methods (evaluated with the total work held fixed) have a very large number of stages.
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McLachlan, R.I. Families of High-Order Composition Methods. Numerical Algorithms 31, 233–246 (2002). https://doi.org/10.1023/A:1021195019574
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DOI: https://doi.org/10.1023/A:1021195019574