ADAPTIVE LINEAR-EQUATION SOLVERS IN CODES FOR LARGE STIFF SYSTEMS OF ODES

Iterative linear equation solvers have been shown to be effective in c odes for large systems of stiff initial-value problems for ordinary di fferential equations (ODEs). While preconditioned iterative methods ar e required in general for efficiency and robustness, unpreconditioned methods may be cheaper over some ranges of the interval of integration . In this paper, a strategy is developed for switching between unpreco nditioned and preconditioned iterative methods depending on the amount of work being done in the iterative solver and properties of the syst em being solved. This strategy is combined with a ''type-insensitive'' approach to the choice of formula used in the ODE code to develop a m ethod that makes a smooth transition between nonstiff and stiff regime s in the interval of integration. As expected, it is found that for so me large systems of ODEs, there may be a considerable saving in execut ion time when the type-insensitive approach is used. If there is a reg ion of the integration that is ''mildly'' stiff, switching between unp reconditioned and preconditioned iterative methods also increases the efficiency of the code significantly.