On symmetric-conjugate composition methods in the numerical integration of differential equations

Blanes, S.; Casas, F.; Chartier, P.; Escorihuela-Tomàs, A.

doi:10.1090/mcom/3715

On symmetric-conjugate composition methods in the numerical integration of differential equations
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by S. Blanes, F. Casas, P. Chartier and A. Escorihuela-Tomàs;

Math. Comp. 91 (2022), 1739-1761

DOI: https://doi.org/10.1090/mcom/3715

Published electronically: December 22, 2021

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Abstract:

We analyze composition methods with complex coefficients exhibiting the so-called “symmetry-conjugate” pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative properties when projected on the real axis and we compare them with the usual left-right palindromic compositions. New schemes within this family up to order 8 are proposed and their efficiency is tested on several examples. Our analysis shows that higher-order schemes are more efficient even when time step sizes are relatively large.

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On symmetric-conjugate composition methods in the numerical integration of differential equations
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Abstract: