An evaluation of some new cyclic linear multistep formulas for stiff ODEs

Abstract

We evaluate several sets of cyclic linear multistep formulas (CLMFs). One of these sets was derived by Tischer and Sacks-Davis. Three new sets of formulas have been derived and we present their characteristics. The formulas have been evaluated by comparing the performance of four versions of a code which implements CLMFs. The four versions are very similar and each version implements one of the sets of CLMFs being studied. We compare the performance of these codes with that of a widely used code, LSODE. One of the new sets of CLMFs is not only much more efficient in solving stiff problems that have a Jacobian with eigenvalues close to the imaginary axis but is almost as efficient as LSODE in solving other problems. This is a significant improvement over the ony other CLMF code available, STINT from Tendler, Bickart, and Picel.