In approximating the solution to a first-order [[ordinary differential equation]], suppose one knows the solution points <math>y_0</math> and <math>y_1</math> at times <math>t_0</math> and <math>t_1</math>. By fitting a cubic polynomial to the points and their derivatives (gottenobtained throughfrom the differential equation), one can predict a point <math>\tilde{y}_2</math> by [[Extrapolation|extrapolating]] to a future time <math>t_2</math>. Using the new value <math>\tilde{y}_2</math> and its derivative there, <math>\tilde{y}^'_2</math> along with the previous points and their derivatives, one can then better [[Interpolation|interpolate]] the derivative between <math>t_1</math> and <math>t_2</math> to get a better approximation <math>y_2</math>. The interpolation and subsequent integration of the differential equation constitute the corrector step.
