PARTIALLY IMPLICIT METHOD FOR LARGE STIFF SYSTEMS OF ODES WITH ONLY FEW EQUATIONS INTRODUCING SMALL TIME-CONSTANTS

Frequently the stiffness of large initial value problems in ordinary differential equations is due to only a few distinct equations introducing the small time-constants. It seems inefficient to solve these problems with the fully implicit methods suggested in a variety of papers. The method suggested in this paper combines an implicit and an explicit formula in an obvious manner. Local rational extrapolation is used to automatically control accuracy and step size. The explicit part agrees with the Bulirsch-Stoer method and consequently only few changes are necessary in Bulirsch-Stoer programs to facilitate the alternative use of the method described.