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Re:Faster Python with Guido van Rossum by ChrisRackauckas on Thursday October 07, 2021 @05:38PM (#28792445)
>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/#Symp... . Also Magnus methods https://diffeq.sciml.ai/stable/solvers/nonautonomous_linear_... and exponential integrators 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 . A lot of this specialized matrix exponential stuff is rather fun, for example see https://github.com/SciML/ExponentialUtilities.jl/pull/64

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