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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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Implicit SSP Methods #97

Open ChrisRackauckas opened 7 years ago

ChrisRackauckas commented 7 years ago

While on the Implicit RK rampage, I plan to pick up methods specific for hyperbolic PDEs.

http://www.sciencedirect.com/science/article/pii/S0168927407001651 http://people.maths.ox.ac.uk/macdonald/imssp.pdf Maybe even https://arxiv.org/pdf/1510.04303.pdf

SDIRK will follow the setup that was created by the IE/Trapezoid/TRBDF2 methods.

ChrisRackauckas commented 7 years ago

Of these the ones which seem like they could be efficient are the higher order SDIRK

http://www.sciencedirect.com/science/article/pii/S0168927407001651