Abstract
This report considers the effect of adding a simple time filter to the fully implicit or backward Euler method. The approach is modular and requires the addition of only one line of additional code. Error estimation and variable time step are straightforward and the individual effect of each step is conceptually clear. The backward Euler method with a curvature reducing time filter induces an equivalent 2-step, second order, A-stable, linear multistep method.
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Communicated by Antonella Zanna Munthe-Kaas.
Partially supported by NSF Grant DMS 1522574. Partially supported by NSF Grant DMS 1522267 and NSF Grant CBET-CDS&E 1609120.
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Guzel, A., Layton, W. Time filters increase accuracy of the fully implicit method. Bit Numer Math 58, 301–315 (2018). https://doi.org/10.1007/s10543-018-0695-z
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DOI: https://doi.org/10.1007/s10543-018-0695-z