Rosenbrock – Kaps&Rentrop’s parameters

Kaps & Rentrop (Generalized Runge Kutta methods of order four with stepsize control for stiff ODE’s) derived a pair of coefficients based on two different values of gamma. Their original representation does not appear to account for the scaling of the identity matrix, nor does it include the coefficients for the error calculations. In their book on stiff ODEs, Hairer & Wanner do present the coefficients in a format that can be readily used with the Generalized Rosenbrock formulation. Adjustable step size control can be achieved using the Kaps-Rentrop algorithm. Hairer & Wanner’s coefficients can be found here.

The Kaps-Rentrop coefficients for gamma = 0.395 (referred to as GRK4A) are as follows:

A21= 0.1108860759493671E01
A31= 0.2377085261983360E01
A32= 0.1850114988899692
C21=-0.4920188402397641E01
C31= 0.1055588686048583E01
C32= 0.3351817267668938E01
C41= 0.3846869007049313E01
C42= 0.3427109241268180E01
C43=-0.2162408848753263E01
B1= 0.1845683240405840E01
B2= 0.1369796894360503
B3= 0.7129097783291559
B4= 0.6329113924050632
e1= 0.4831870177201765E-01
e2=-0.6471108651049505
e3= 0.2186876660500240
e4=-0.6329113924050632
GAMMA= 0.3950000000000000
c2= 0.4380000000000000
c3= 0.8700000000000000
d1= 0.3950000000000000
d2=-0.3726723954840920
d3= 0.6629196544571492E-01
d4= 0.4340946962568634