10. ABSTRACT (Maxm 200 W, In solving stiff systems of ordinary differential equations using BDF methods, Jacobians needed for quasi-Newton iteration are frequently computed using finite differences. Round-olf errors in the finite-difference approximation can lead to Newton failures forcing the code to choose its time steps based on "stabili y" rather than accuracy considerations. When standard stepsize control is used the code can experience thrashing which increases the total n ex of time steps,Jacobian evaluations, & function evaluations. In this paper we investigate this situation, explaining some surprising time step selection behavior produced by the standard control mechanism. A new control mechanism is proposed which attempts to find & use a "stability" stepsize. A comparison of the new strategy with the standard strategy & with two PI controllers introduced earlier is made using the stiff test set.
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