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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Multi Rate Methods #1195

Open kanav99 opened 4 years ago

kanav99 commented 4 years ago
  1. Rice, 1960 - https://nvlpubs.nist.gov/nistpubs/jres/64B/jresv64Bn3p151_A1b.pdf
  2. Skelboe, Multirate BDF, 1989 - https://www.researchgate.net/publication/223287901_Stability_properties_of_backward_differentiation_multirate_formulas
  3. Günther and Rentrop, Multirate ROW Method - 1993 - https://www.sciencedirect.com/science/article/abs/pii/016892749390133C
  4. Löhner, Morgan, Zienkiewicz - Explicit Multirate - 1984 - https://www.sciencedirect.com/science/article/pii/0045782584901592
  5. Kirby - Multirate Forward Euler - 2002 - https://www.researchgate.net/publication/220577091_On_the_convergence_of_high_resolution_methods_with_multiple_time_scales_for_hyperbolic_conservation_laws
  6. Constantinescu and Sandu - Multirate RK - 2007 - https://core.ac.uk/reader/10676122
  7. B. Senya, J. Lambrechtsa, T. Toulorgea, V. Legata, J.-F. Remaclea - parallel Multi RK - 2014 - https://perso.uclouvain.be/thomas.toulorge/paper_jcp_multirate.pdf

Adding more as I see prominent papers

ChrisRackauckas commented 4 years ago

From @thomasgibson:

How do these compare? I think the first set is a review article and might contain some of these others.

ChrisRackauckas commented 4 years ago

The first paper comes down to https://www.sciencedirect.com/science/article/pii/S0377042708004147 which is supposed to be an improvement on Constantinescu and Sandu.

https://www.sciencedirect.com/science/article/abs/pii/S0168927498000518 shows up a lot.

ChrisRackauckas commented 4 years ago

It looks like extMIS might be the generalization that could be useful in this context.

https://www.sciencedirect.com/science/article/pii/S0377042719305461