Pseudo-symplectic methods

[ranocha]

Pseudo-symplectic methods conserve quadratic invariants to a higher order of accuracy than their classical order of accuracy.

• [ ] Capuano, Francesco, Gennaro Coppola, Luis Rández, and Luigi de Luca. "Explicit Runge–Kutta schemes for incompressible flow with improved energy-conservation properties." Journal of Computational Physics 328 (2017): 86-94.
  • [x] 3p5q(4)
  • [x] 4p7q(6)
• [ ] Calvo, Manuel, M. P. Laburta, Juan I. Montijano, and Luis Rández. "Approximate preservation of quadratic first integrals by explicit Runge–Kutta methods." Advances in Computational Mathematics 32 (2010): 255-274.
• [ ] Aubry, Anne, and Philippe Chartier. "Pseudo-symplectic Runge-Kutta methods." BIT Numerical Mathematics 38 (1998): 439-461.
  • [x] 3p6q(5) from Fig. 4.1
• [ ] Stepanov, Misha. "Eight-stage pseudo-symplectic Runge-Kutta methods of order (4, 8)." arXiv preprint arXiv:2301.09335 (2023).

[MarcoArtiano]

3p5q(4), 4p7q(6) and 3p6q(5) have been added with the following PR: https://github.com/SciML/OrdinaryDiffEq.jl/pull/2174