Alignment between “Recommended Methods” and the polyalgorithms

[prbzrg]

IMO, there should be alignment between “Recommended Methods” section in docs and the polyalgorithms. For example, the polyalgorithm doesn't include GPU solvers, but they are recommended. Or Feagin14 is recommended for high accuracy solving, but the polyalgorithm doesn't use it.

https://docs.sciml.ai/DiffEqDocs/dev/solvers/ode_solve/#Recommended-Methods

https://github.com/SciML/DifferentialEquations.jl/blob/master/src/ode_default_alg.jl

[ChrisRackauckas]

The polyalgorithm constrains itself to a smaller set of algorithms to keep compilation time down, and prefers robustness over performance over a wide range of problems. Because of that, it sometimes deviates from the most optimal to something slightly less optimal in order to cut the number of algorithms in the list.

[prbzrg]

If DifferentialEquations includes all algorithms. (?) Can't we add an option to choose between "most optimal" or "best tradeoff"? Maybe in alg_hints

[ChrisRackauckas]

Or just make those algorithms like SciML/OrdinaryDiffEq.jl#2103