Eight-stage pseudo-symplectic Runge-Kutta methods of order (4, 8)

Misha Stepanov

Eight-stage pseudo-symplectic Runge-Kutta methods of order (4, 8)

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arxiv 2301.09335 v4 pith:ZN4EP34S submitted 2023-01-23 math.NA cs.NA

Misha Stepanov This is my paper · ORCID

classification math.NAcs.NA

keywords ordermethodspseudo-symplecticrunge-kuttastageassumptionsderiveddimensional

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Using simplifying assumptions that are related to the time reversal symmetry, a 1-dimensional family of 8-stage pseudo-symplectic Runge-Kutta methods of order (4, 8), i.e., methods of order 4 that preserve symplectic structure up to order 8, is derived. An example of 7-stage method of order (4, 9) is given.

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The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems
math.NA 2025-04 reject novelty 6.0 of 10

The claimed explicit symplectic integrators for general nonseparable Hamiltonians are not actually symplectic: the proof's point-dependent projection invalidates it, and H=pq gives a direct counterexample.

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