[inasio]

I was expecting a mention of symplectic ODE solvers, although perhaps that was beyond the scope of the blog post. For Hamiltonian ODEs, you can design methods that explicitly preserve energy, outperforming more generic methods.

[ChrisRackauckas]

Yeah, that's a separate post https://scicomp.stackexchange.com/questions/29149/what-does-.... I wanted to keep this post as simple as possible. If you could show cases where explicit Runge-Kutta methods outperform (by some metrics) implicit Runge-Kutta methods, then it leads to a whole understanding of "what matters is what you're trying to measure". And then yes, symplectic integrators are for long time integrations (explicit RK methods will how lower error for shorter time, so its specifically longer time integrations on symplectic manifolds, though there are implicit RK methods which are symplectic but ... tradeoff tradeoff)