The
W-method as presented by Steihaug & Wolfbrandt involves the matrix multiplication of the Jacobian with the ki’s at each step. Shampine (Implementation of Rosenbrock Algorithms, ACM Transactions on Mathematical Software, Vol. 8, No. 2, 1982, pp 93-113) also suggests “conditioning” the A matrix to avoid difficulties during the LU-decomposition. Shampine recommends working with the following format for A:
To avoid the matrix multiplication on the right hand side, the following re-arranged format is typically used for coding the 2-stage Rosenbrock method:
An intermediate step is required where the matrix g2 is calculated, from which k2 is later determined.
