Partial revert for ROW docs and fix of tableau docstrings

[termi-official]

xref https://github.com/SciML/OrdinaryDiffEq.jl/commit/f8f8307cf3717ae985c6ef165ef2bc8d60947bfc#r142723908 for the discussion and thanks for pointing this out @cwittens . Can you double check that we get it right this time?

[cwittens]

If I am not mistaken the W in W-methods doesnt not stand for Wanner. As far as I see it, you can have Rosenbrock-Wanner-methods or short Rosenbrock-methods see german Wiki. And special kinds of Rosenbrock-Wanner-methods (or short Rosenbrock-methods) are called W-methods, after Wolfbrandt, if they fullfill another condition (one can use an approximation of the Jacobian without order loss). See the Introduction of this Paper.

So all the methods are ROW (Rosenbrock-Wanner), but for example ROS2S is also a W-method, but ROS2 isnt.

@ranocha can you maybe confirm / deny my explanation.

[oscardssmith]

oh, that's awful. They really should be called ROWW or something to avoid confusion.

[ChrisRackauckas]

Wolfbrandt and Wanner should just have a cage match for naming rights.

[termi-official]

If I am not mistaken the W in W-methods doesnt not stand for Wanner. As far as I see it, you can have Rosenbrock-Wanner-methods or short Rosenbrock-methods see german Wiki.

Wait, now I am a confused. I thought he difference between Rosenbrock and Rosenbrock-Wanner methods is that the latter reuses the same linear system in all stages while the former builds a new linear system for each stage. The interpretation of these methods is as in doing a single Newton vs a single Quasi-Newton step and taking the result as the solution approximation.

And special kinds of Rosenbrock-Wanner-methods (or short Rosenbrock-methods) are called W-methods, after Wolfbrandt, if they fullfill another condition (one can use an approximation of the Jacobian without order loss). See the Introduction of this Paper.

So all the methods are ROW (Rosenbrock-Wanner), but for example ROS2S is also a W-method, but ROS2 isnt.

I see. Thanks for pointing this out.

[ChrisRackauckas]

Wait, now I am a confused. I thought he difference between Rosenbrock and Rosenbrock-Wanner methods is that the latter reuses the same linear system in all stages while the former builds a new linear system for each stage. The interpretation of these methods is as in doing a single Newton vs a single Quasi-Newton step and taking the result as the solution approximation.

Yes. That's the technical difference. I never realized it didn't stand for Wanner though. What a phony.

[termi-official]

So, next round of fixes I guess.

rosenbrock_wanner_docstring -> rosenbrock_wolfbrandt_docstring

and

https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/doc_utils.jl#L135 -> "Rosenbrock-W(olfbrandt) Method. "

?

oh, that's awful. They really should be called ROWW or something to avoid confusion.

Seems like Collin already started :) https://github.com/SciML/OrdinaryDiffEq.jl/blob/762a742762b8238a045b2da54a5e599a0a9194ee/src/generic_rosenbrock.jl#L1267

[ranocha]

As far as I can tell, @cwittens is right. If you want full clarity, you could use

rosenbrock_wanner_docstring -> rosenbrock_wanner_wolfbrandt_docstring or rosenbrock_wanner_wmethod_docstring

or something like that.