A NEW VERY SIMPLE EXPLICIT METHOD FOR THE INTEGRATION OF MILDLY STIFF ORDINARY DIFFERENTIAL-EQUATIONS

A new explicit, first-order method with improved stability properties for the integration of stiff ODE systems is developed. The new method is very simple and requires only two derivative evaluations per step (like the second-order explicit Runge-Kutta method) but has a stability region that is almost four times larger than that of RK2. Furthermore, error control/variable-step integration for the new method is easy. The new method is more efficient than RK2 for typical stiff problems (including method-of-lines problems). It is most efficient on mildly and moderately stiff problems when low or intermediate accuracy is desired. Furthermore, when limited computer memory is available, the new method offers a valuable alternative to the implicit methods (especially for very large stiff systems). In addition, the use of global extrapolation is shown to improve the accuracy of the new method and to offer global error estimates. © 1990.