Stabilizing predictors for weakly unstable correctors
Hans J. Stetter · Mathematics of Computation · 1965
should not be used for the numerical integration of y' = f(x, y) if ff < 0 along the true solution y(x) although the solution of (1) converges to y(x) for fixed finite x as h 0 (see, e.g., [1]). In fact, rapid oscillations, with an amplitude increasing exponentially as the numerical integration proceeds, will supersede the values approximating y(x) and eventually destroy the meaningfulness of the computation. This weak unstability occurring with (1) and similar algorithms has been well analyzed (e.g., [1, p. 248 ff.]) and procedures have been suggested to weaken its effect (e.g., [2]). We will show in this paper that it is quite easy to completely eliminate its cause: The combination of a judiciously chosen predictor with the weakly unstable corrector constitutes a strongly stable algorithm if the corrector is not iterated.