New tableaux for rodas4p, now rodas4p2

[gstein3m]

Would it be possible to add a new tableaux for a rodas4p2 method, which is an improvement of rodas4p, see https://link.springer.com/chapter/10.1007%2F978-3-030-53905-4_6

#-- Rodas4P2
gamma = convert(T,1//4)
a21= convert(T,3.000000000000000)
a31= convert(T,0.906377755268814)
a32=-convert(T,0.189707390391685)
a41= convert(T,3.758617027739064)
a42= convert(T,1.161741776019525)
a43=-convert(T,0.849258085312803)
a51= convert(T,7.089566927282776)
a52= convert(T,4.573591406461604)
a53=-convert(T,8.423496976860259)
a54=-convert(T,0.959280113459775)

C21= convert(T,-12.00000000000000)
C31= convert(T,-6.354581592719008)
C32= convert(T, 0.338972550544623)
C41= convert(T,-8.575016317114033)
C42= convert(T,-7.606483992117508)
C43= convert(T,12.224997650124820)
C51= convert(T,-5.888975457523102)
C52= convert(T,-8.157396617841821)
C53= convert(T,24.805546872612922)
C54= convert(T,12.790401512796979)
C61= convert(T,-4.408651676063871)
C62= convert(T,-6.692003137674639)
C63= convert(T,24.625568527593117)
C64= convert(T,16.627521966636085)
C65= convert(T,-5.714285714285718)

c2=convert(T2,0.750000000000000)
c3=convert(T2,0.321448134013046)
c4=convert(T2,0.519745732277726)
d1=convert(T, 0.250000000000000)
d2=convert(T,-0.500000000000000)
d3=convert(T,-0.189532918363016)
d4=convert(T, 0.085612108792769)

h21= convert(T, -5.323528268423303)
h22= convert(T,-10.042123754867493)
h23= convert(T, 17.175254928256965)
h24=-convert(T, -5.079931171878093)
h25= convert(T, -0.016185991706112)
h31= convert(T, 6.984505741529879)
h32=-convert(T, 6.914061169603662)
h33= convert(T, -0.849178943070653)
h34= convert(T, 18.104410789349338)
h35=-convert(T, -3.516963011559032)

[ChrisRackauckas]

Yes! Just add a new RodasTableau:

https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/tableaus/rosenbrock_tableaus.jl#L296-L349

and all of the perform_step! stuff will work. For developer documentation on the ODE solver, see:

http://devdocs.sciml.ai/latest/contributing/adding_algorithms/

[dynamic-queries]

@ChrisRackauckas The tableau seems to be already in the package. https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/tableaus/rosenbrock_tableaus.jl#L351-L403

[ChrisRackauckas]

Needs docs

[jchuharski]

I think we have these docs now @oscardssmith pinging myself to close.