Misha Stepanov | publications | arXiv (2023)

M. Stepanov, Eight‑stage pseudo‑symplectic Runge–Kutta methods of order (4, 8), arXiv: 2301.09335 (2023).

DOI: 10.48550/arXiv.2301.09335

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.