More Runge-Kutta Methods for (Hyperbolic) PDEs

[ranocha]

Here are some additional articles describing/investigating/developing Runge-Kutta methods, especially for hyperbolic PDEs:

• Higueras, Roldan (2019) Added low storage SSPRK53 #581 WIP : Implementation of SSPRK53_2N2 #584 and missing the last.
• Conde, Fekete, Shadid (2018) (adaptive) add SSPRK43, cf. #493 #1283
• Kubatko, Yeager, Ketcheson (2014) Implemented KYKDGSSPRK3S2 #669 implemented KYK SSPRK42 #1095 still a few more to do
• Parsani, Ketcheson, Deconinck (2013) Low storage methods: New files and 2 methods of Parsani, Ketcheson, Deconinck #648 Parsani, Ketcheson, Deconinck: 2nd and 3rd order methods #658
• Niegemann, Diehl, Busch (2012), especially Table 3 Implemented NDBLSRK124 from Niegemann, Diehl, Busch (2012) #611, Implemented NDBLSRK134 from Niegemann, Diehl, Busch (2012) #614, Implemented NDBLSRK144 from Niegemann, Diehl, Busch (2012) #616
• Bernardini, Pirozzoli (2009) Implemented ORK25-6 from Bernardini, Pirozzoli (2009) #600
• Tselios, Simos (2007) Implemented TSLDDRK74 Tselios, Simos (2007) #637
• Toulorge, Desmet (2012) Implemented DGLDDRK73_C from Toulorge, Desmet (2012) #641, Implemented DGLDDRK84_C from Toulorge, Desmet (2012) #642, Implemented DGLDDRK84_F from Toulorge, Desmet (2012) #644
• Berland, Bogey, Bailly (2006) RK46-NL Implementation #598
• Calvo, Franco, Randez (2004) Implemented LDDRK46 from Calvo, Franco, Randez (2004) #607
• Kennedy, Carpenter, Lewis (2000)
• Mead, Renaut (1999)
• Stanescu, Habashi (1998) LDDRK 6-stage 4th order #596 Implemented the Stanescu, Habashi 5stage 2nd order method #1051 (the two step RK methods are left which were moved to Two-Step Runge-Kutta Methods #117)
• Hadjimichael, Ketcheson, Lóczi, and Németh (2016) (multistep, adaptive, moved to Explicit Multistep SSP Methods #945)

These methods do not necessarily have high-priority but may be implemented. There are also many other methods.

[ChrisRackauckas]

Thanks! Since we have good infrustructure for Runge-Kutta methods I think it's best to leave this as an introductory issue (this is a good "first algorithm" for potential GSoC students!)

[ChrisRackauckas]

There's this one as well: https://arxiv.org/abs/1806.08693

[ranocha]

There's this one as well: https://arxiv.org/abs/1806.08693

I've added it to the list.

[ChrisRackauckas]

And a new one: https://arxiv.org/abs/1809.04807

[ranocha]

And a new one: https://arxiv.org/abs/1809.04807

Thanks. I've added that as well to the list.

[dgan181]

I have tried to implement the first method in the list given above in #581. I'd like to know if it is alright.

[ranocha]

Thanks, @dgan181. You implemented the method SSPRK53_2N1 of Higueras and Roldan as SSPRK53_2N, didn't you? It may be good to add also the other scheme SSPRK53_2N2 (eq. (60) of Higueras and Roldan).

It would be good to add the new citation for SSPRK53_2N (or SSPRK53_2N1 and SSPRK53_2N2 if both are added) to https://github.com/JuliaDiffEq/juliadiffeq.github.io/blob/master/citing.md.

[dgan181]

@ranocha I tried implementing the second method here #584 . Once that is resolved, I will add the new citations.

[arnav-t]

I'm implementing RK46-NL from Berland, Bogey, Bailly (2006)

[ChrisRackauckas]

Merging the discussion of #415. @dgan181 is doing Conde, Fekete, Shadid (2018)