Symplectic Integration with Processing: A General Study

1 January 1999

journal article
research article
Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing

Vol. 21 (2) , 711-727
https://doi.org/10.1137/s1064827598332497

Abstract

The number of conditions to be satisfied by the operators K and P in symplectic integrators with processing, given by e(P)e(hK)e(P), is determined for a Hamiltonian of the form H = A + B. The conditions for K are explicitly written up to order six and used to obtain more efficient methods with fewer evaluations per step than other symplectic integrators. Special cases in which the number of conditions for the kernel is drastically reduced are also studied. It is shown that the kernel completely determines the optimal method one can obtain by processing.

Keywords

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