High Quality Content by WIKIPEDIA articles! In mathematics, particularly numerical analysis, a predictor-corrector method is an algorithm that proceeds in two steps. First, the prediction step calculates a rough approximation of the desired quantity. Second, the corrector step refines the initial approximation using another means. In approximating the solution to a first-order ordinary differential equation, suppose one knows the solution points y0 and y1 at times t0 and t1. By fitting a cubic polynomial to the points and their derivatives (obtained from the differential equation), one can predict a point tilde{y}_2 by extrapolating to a future time t2. Using the new value tilde{y}_2 and its derivative there, tilde{y}^'_2 along with the previous points and their derivatives, one can then better interpolate the derivative between t1 and t2 to get a better approximation y2. The interpolation and subsequent integration of the differential equation constitute the corrector step.

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