Rosenbrock – Shampine’s parameters

Shampine (Implementation of Rosenbrock Methods) derived a set of coefficients for the Rosenbrock methods, with a gamma value of 0.5. Presented below are the coefficients for Shampine’s method, with the scaling accounted for direct implementation in the generalized method (ref: here). The generalized Rosenbrock algorithm can be easily implemented with these coefficients.

         A21=2.
         A31=48./25.
         A32=6./25.
         C21=-8.
         C31=372./25.

         C32=12./5.
         C41=-112./125.
         C42=-54./125.
         C43=-2./5.
         B1=19./9.
         B2=1./2.
         B3=25./108.
         B4=125./108.
         E1=17./54.
         E2=7./36.
         E3=0.
         E4=125./108.
         GAMMA=.5
         C2= 0.1000000000000000E01
         C3= 0.6000000000000000
         D1= 0.5000000000000000
         D2=-0.1500000000000000E01
         D3= 0.2420000000000000E01
         D4= 0.1160000000000000