Conjugate-symplecticity properties of Euler--Maclaurin methods and their implementation on the Infinity Computer
F. Iavernaro; F. Mazzia; M. S. Mukhametzhanov; Ya. D. Sergeyev · 2018 · arXiv
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Abstract (excerpt)
Multi-derivative one-step methods based upon Euler-Maclaurin integration formulae are considered for the solution of canonical Hamiltonian dynamical systems. Despite the negative result that simplecticity may not be attained by any multi-derivative Runge--Kutta methods, we show that the Euler-MacLaurin method of order p is conjugate-symplectic up to order p+2. This feature entitles them to play a role in the context of geometric integration and, to make their implementation competitive with the existing integrators, we explore the possibility of computing the underlying higher order derivative
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Metadata source: arXiv