Support for affine functions to bypass nonlinear solver if applicable

[termi-official]

Is your feature request related to a problem? Please describe.

We have support for linear functions (via LinearOperator) to partially bypass some of the nonlinear solver logic. Affine functions (via AffineOperator) currently do not bypass this logic.

Describe the solution you’d like

For linear and affine ODE problems we can completely skip the Newton logic for a large variety of stiff solvers. This can save us some memory for large problems coming from e.g. PDE semidiscretizations.

Describe alternatives you’ve considered

Right now the only way I see is to go with a custom integrator+custom solver type similar to https://github.com/SciML/SimpleDiffEq.jl/ . We can probably setup some benchmarks on this matter to explore how much the gains are.

Additional context

Nope.

[ChrisRackauckas]

I swear I had an issue on this in here somewhere but I can't find it. But yes, this needs to be done.