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SciML / OrdinaryDiffEq.jl

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
https://diffeq.sciml.ai/latest/
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ROS2S method #2409

Open termi-official opened 2 months ago

termi-official commented 2 months ago

What kind of problems is it mostly used for? Please describe.

Semi-discretizations of $H^1 \times L_2$ solution fields.

Describe the algorithm you’d like

Stabilized Rosenbrock with special linear solution handling of the $L_2$ fields (Schur-complement reduction). Could also well for some stiff ODEs without special structure.

Other implementations to know about

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References

Original paper is here https://doi.org/10.1016/j.apnum.2012.08.001 . The specialized solver is described here https://doi.org/10.1016/j.cma.2009.12.011 and can probably be reused across all other Rosenbrock methods.

ChrisRackauckas commented 2 months ago

Any reason why this would be preferred over the new Ros23W scheme?

termi-official commented 2 months ago

Do you mean Rodas23W? If so, then I am not sure if it is also stiffly accurate and this would be the selling point of ROS2S.

ChrisRackauckas commented 2 months ago

It is