The Taming of a Co-polymerization Problem with VODE

Abstract

The dimensionless mathematical model describes a polymer granule in a heterogeneous copolymerization process, which produces one of several important polyolefins with Ziegler-Natta catalyst. We give numerical results and explain how we have recently improved the performance of our code for simulating this process. In particular, we use the ODE (ordinary differential equation) solver VODE, as we did earlier. However, our newer co-polymerization code is both much faster and more robust than the previous version, which we described elsewhere. As before, the mathematical model corrects previously published models of others. We also include comments on the model, explain how we have used a band matrix approximation to the Jacobian to achieve the current level of performance, and provide some insight to our computational results. Finally, we include CPU timing for VODE, LSODE, and DASSL, which supports the choice of VODE for this problem.