Split Shooting methods into subpackage

[ErikQQY]

Continue #214

[github-actions]

Benchmark Results

	master	7783f84...	master/7783f84e1c57bb...
Simple Pendulum/IIP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK2()	6.44 ± 0.16 ms	6.54 ± 0.16 ms	0.984
Simple Pendulum/IIP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK3()	2.33 ± 0.053 ms	2.34 ± 0.05 ms	0.996
Simple Pendulum/IIP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK4()	0.81 ± 0.017 ms	0.816 ± 0.016 ms	0.993
Simple Pendulum/IIP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK5()	0.859 ± 0.02 ms	0.873 ± 0.02 ms	0.983
Simple Pendulum/IIP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK6()	0.979 ± 0.022 ms	0.986 ± 0.017 ms	0.993
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.38 ± 0.18 ms	1.39 ± 0.17 ms	0.994
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	2.66 ± 0.19 ms	2.68 ± 0.17 ms	0.993
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0371 ± 0.013 s	0.0376 ± 0.013 s	0.987
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.0451 ± 0.012 s	0.0444 ± 0.011 s	1.02
Simple Pendulum/IIP/Shooting(Tsit5())	0.208 ± 0.013 ms	0.209 ± 0.014 ms	0.995
Simple Pendulum/OOP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK2()	0.0394 ± 0.00068 s	0.04 ± 0.00075 s	0.985
Simple Pendulum/OOP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK3()	11.4 ± 0.13 ms	11.6 ± 0.14 ms	0.979
Simple Pendulum/OOP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK4()	3.32 ± 0.069 ms	3.35 ± 0.069 ms	0.989
Simple Pendulum/OOP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK5()	3.38 ± 0.085 ms	3.41 ± 0.079 ms	0.993
Simple Pendulum/OOP/BoundaryValueDiffEq.BoundaryValueDiffEqMIRK.MIRK6()	3.52 ± 0.088 ms	3.56 ± 0.099 ms	0.99
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.94 ± 2.8 ms	3.82 ± 2.8 ms	1.03
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	6.84 ± 3.2 ms	6.53 ± 2.6 ms	1.05
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.141 ± 0.0049 s	0.141 ± 0.009 s	1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.163 ± 0.013 s	0.169 ± 0.012 s	0.966
Simple Pendulum/OOP/Shooting(Tsit5())	0.751 ± 0.18 ms	0.764 ± 0.13 ms	0.984
time_to_load	9.34 ± 0.042 s	9.87 ± 0.024 s	0.946

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[ErikQQY]

Ready to go now

[ErikQQY]

There are still some questions though:

1. Are we going to leave the extension algorithms from ODEInterface.jl in BoundaryValueDiffEq.jl or make them into a subpackage too?
2. I noticed NonlinearSolve.jl is putting SimpleNonlinearSolve.jl into a subpackage, should we also do the same?

[ChrisRackauckas]

I noticed SciML/NonlinearSolve.jl#456 (comment), should we also do the same?

No harm either way. I think the key is to make a core that is very lean.

Are we going to leave the extension algorithms from ODEInterface.jl in BoundaryValueDiffEq.jl or make them into a subpackage too?

Having them as extensions is fine if the core is lean.