Refactor FIRK solvers

[ErikQQY]

• Add precompilation options for Lobatto and Radau solvers, but precompiling all of them seems to take a long time, so just set them as false for now
• Previous tolerance for nested nonlinear solving is bad, change it to nothing as default so that NonlinearSolve.jl can choose automatically
• Some variables and functions in some functions are not used, so cleaned up a little
• Some functions are not optimal, improve their performance
• Unify the interpolant evaluation for MIRK and FIRK methods

[github-actions]

Benchmark Results

	master	ac46c48...	master/ac46c48389ac67...
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK2()	6.59 ± 0.22 ms	6.72 ± 0.28 ms	0.981
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK3()	2.37 ± 0.084 ms	2.39 ± 0.11 ms	0.99
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK4()	0.826 ± 0.033 ms	0.834 ± 0.038 ms	0.991
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK5()	0.875 ± 0.043 ms	0.888 ± 0.049 ms	0.986
Simple Pendulum/IIP/BoundaryValueDiffEq.MIRK6()	0.989 ± 0.038 ms	1.01 ± 0.041 ms	0.982
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.41 ± 0.13 ms	1.41 ± 0.13 ms	0.994
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	2.76 ± 0.25 ms	2.77 ± 0.23 ms	0.995
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0375 ± 0.0063 s	0.0378 ± 0.0063 s	0.991
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.122 ± 0.0053 s	0.122 ± 0.0034 s	1
Simple Pendulum/IIP/Shooting(Tsit5())	0.209 ± 0.0086 ms	0.209 ± 0.0077 ms	1
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK2()	0.0403 ± 0.0019 s	0.0419 ± 0.0011 s	0.962
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK3()	11.7 ± 0.25 ms	12.1 ± 0.24 ms	0.968
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK4()	3.4 ± 0.084 ms	3.49 ± 0.12 ms	0.974
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK5()	3.47 ± 0.098 ms	3.57 ± 0.11 ms	0.973
Simple Pendulum/OOP/BoundaryValueDiffEq.MIRK6()	3.63 ± 0.12 ms	3.69 ± 0.12 ms	0.984
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.71 ± 0.82 ms	3.58 ± 1.1 ms	1.04
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	6.58 ± 1.5 ms	6.34 ± 1.8 ms	1.04
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.135 ± 0.015 s	0.134 ± 0.01 s	1.01
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.419 ± 0.0067 s	0.413 ± 0.0052 s	1.01
Simple Pendulum/OOP/Shooting(Tsit5())	0.798 ± 0.027 ms	0.749 ± 0.039 ms	1.06
time_to_load	6.44 ± 0.038 s	5.66 ± 0.043 s	1.14

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).

[ChrisRackauckas]

You should probably just split it to a subpackage, i.e. lib/BoundaryDiffEqFIRK, and then you can set it to precompile, but it does not have to be in the standard BounaryDiffEq load. The plan should be to do this split with all of the solvers.

[ErikQQY]

Yeah, splitting BoundaryValueDiffEq.jl into subpackages like what we've done in OrdinaryDiffEq.jl is on my TODO list, so let's leave the precompile stuff into splitting part and get the others in? Since the Shooting, MIRK and FIRK are separately implemented in BoundaryValueDiffEq.jl, I can get that done today