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OrdinaryDiffEq.jl reviews and mentions
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Modern Numerical Solving methods
There has been a lot of research in Runge Kutta methods in the last couple decades which resulted in all kind of specialized Runge Kutta methods. You have high order ones, RK methods for stiff problems, embedded RK methods which benefit from adaprive step size control, RK-Nystrom methods for second order Problems, symplectic RK methods which preserve energy (eg. hamiltonian) ando so on. If you are interested in the numerics and the use cases I highly recommend checking out the Julia Libary OrdinaryDiffEq (https://github.com/SciML/OrdinaryDiffEq.jl). If you look into the documentation you find A LOT of implemented RK methods for all kind of use cases.
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Why Fortran is a scientific powerhouse
Project.toml or Manifest.toml? Every package has Project.toml which specifies bounds (https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/Proje...). Every fully reproducible project has a Manifest that decrease the complete package state (https://github.com/SciML/SciMLBenchmarks.jl/blob/master/benc...).
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How do the Julia ODE solvers choose/select their initial steps? What formula do they use to estimate the appropriate initial step size?
Yes. If you want to see a robust version of the algorithm you can check out https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/initdt.jl
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SciML/OrdinaryDiffEq.jl is an open source project licensed under GNU General Public License v3.0 or later which is an OSI approved license.
The primary programming language of OrdinaryDiffEq.jl is Julia.
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