>I wonder if open source ODE solvers are getting good high-order symplectic methods by now... Up to 10th order https://diffeq.sciml.ai/stable/solvers/dynamical

>I wonder if open source ODE solvers are getting good high-order symplectic methods by now... Up to 10th order https://diffeq.sciml.ai/stable/solvers/dynamical_solve/#Symplectic-Integrators https://diffeq.sciml.ai/stable/solvers/dynamical_solve/#Symp... . Also Magnus methods https://diffeq.sciml.ai/stable/solvers/nonautonomous_linear_ode/#State-Independent-Solvers https://diffeq.sciml.ai/stable/solvers/nonautonomous_linear_... and exponential integrators https://diffeq.sciml.ai/stable/solvers/split_ode_solve/#OrdinaryDiffEq.jl-2 https://diffeq.sciml.ai/stable/solvers/split_ode_solve/#Ordi... . And the expmv implementations are highly optimized as well: https://github.com/SciML/ExponentialUtilities.jl https://github.com/SciML/ExponentialUtilities.jl . A lot of this specialized matrix exponential stuff is rather fun, for example see https://github.com/SciML/ExponentialUtilities.jl/pull/64 https://github.com/SciML/ExponentialUtilities.jl/pull/64