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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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Higher-Order Rosenbrock Methods #14

Closed ChrisRackauckas closed 7 years ago

ChrisRackauckas commented 7 years ago

Here's one link: https://rotordynamics.wordpress.com/category/rosenbrock-methods/

I'm working on them.

ChrisRackauckas commented 7 years ago

http://www.sciencedirect.com/science/article/pii/S0045793015001905

ChrisRackauckas commented 7 years ago

http://people.cs.vt.edu/asandu/Deposit/bench2.pdf

Benchmarking stiff ode solvers for atmospheric chemistry problems II Rosenbrock solvers

ChrisRackauckas commented 7 years ago

https://link.springer.com/content/pdf/10.1007%2FBF01397096.pdf

That method doesn't seem too good so it can wait.

ChrisRackauckas commented 7 years ago

http://cui.unige.ch/~dimarzo/papers/DIPL93.pdf

The Rodas5 paper

ChrisRackauckas commented 7 years ago

The Kaps Warner do not have error estimators, so the authors use extrapolation (solve with h, then twice with h/2) instead of an embedding. From experience I know this is really bad, so I'm not wasting my time there. Thus this is complete!