New Rosenbrock-type methods of Sandu that favor positivity for chemical reactions

[ranocha]

See Sandu (2000) Time stepping methods that favor positivity for atmospheric chemistry modeling. There are four methods

• A: three-stage, second-order, stiffly accurate, allowing inexact Jacobians
• B: three-stage, second-order, stiffly accurate, one order 3 condition satisfied
• C: three-stage, second-order, allowing inexact Jacobians, one order 3 condition satisfied
• D: four-stage, second-order, stiffly accurate, allowing inexact Jacobians, with an embedded method of order 3

[cwittens]

any successions of how one should name the methods when implementing? Just Sandu2A, Sandau2B, ...?

[cwittens]

I just realized that Methods A-C don't have an embedded method. Does it still make sense to implement them? And method D has an embedded method, but it took ~2000 steps to solve u' = 1.01u between (0,1)

After some changing btilde from [8/3, 1, 1, -1/3] to [0, 0, 0, 1] (originally to check for an potential error/bug), I got it down to 15 steps, but this change seems quite arbitrary. Besides from checking again for potential errors in the implementation, I am not sure how to proceed.

And ROS2 is also given in this paper and it has the same coefficients as in https://github.com/SciML/OrdinaryDiffEq.jl/issues/2112 (and with this the same as in KPP), only the embedded methods is different from the one in KPP. I am thinking of implementing both and checking if both give reasonable solutions.

[ChrisRackauckas]

It's fine, those ones just won't be adaptive.

[ranocha]

Thanks, that would be nice 👍