[Dev] Faster ode solver

[jbcaillau]

@ocots what about having our own internal ODE solver? a standalone RKF54 (with adaptative stepsize) would perfectly do the job, I guess while

• avoiding infinitely long install / precompile of OrdinaryDiffEq (they will break everything into smaller pieces sooner or later...)
• ensuring simplicity and performance plus, possibly, eased access to a tailored AD

See, e.g.

• https://github.com/gwater/RungeKuttaFehlberg.jl/tree/master
• https://github.com/SciML/DiffEqDevTools.jl/blob/master/src/ode_tableaus.jl#L866-L920

[jbcaillau]

@ocots see also (thanks @abavoil): https://github.com/SciML/SimpleDiffEq.jl

[jbcaillau]

@joseph-gergaud when you re-check AD for ODE solvers, please consider using the simple code above
#81 (comment)

[jbcaillau]

@ocots see also #42 (comment)

[jbcaillau]

@ocots what are the issues for a possible move to SimpleDiffEq.jl?

• event usage? (e.g. to plot concatenations)
• other...?

[jbcaillau]

@ocots @joseph-gergaud some standalone ode solvers are now available (without important the whole package), check https://docs.sciml.ai/OrdinaryDiffEq/stable/explicit/Tsit5 (thanks @abavoil):

• to be tested, having an extension only on that (instead of full OrdinaryDiffEq.jl)
• also can be nice to change theo ODE solver to higher precision integrators (Verner...)