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Something similar to these SciML Benchmarks would be nice to have:
- Henon-Heiles Energy Conservation: https://docs.sciml.ai/SciMLBenchmarksOutput/stable/DynamicalODE/Henon-Heiles_energy_conservation_benchmark/
- Quadruple Boson Energy Conservation: https://docs.sciml.ai/SciMLBenchmarksOutput/stable/DynamicalODE/Quadrupole_boson_Hamiltonian_energy_conservation_benchmark/#Quadruple-Boson-Energy-Conservation
- Single Pendulum Comparison (currently broken): https://docs.sciml.ai/SciMLBenchmarksOutput/stable/DynamicalODE/single_pendulums/#Solving-single-pendulums-by-DifferentialEquations.jl
This part of the ProbNumDiffEq.jl documentation shows how we can do energy conservation, and that's what we'd want to evaluate and compare to projection methods and symplectic methods.
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