Predictor-Corrector Method

A predictor-corrector method is a class of algorithms for numerically solving ordinary differential equations by finding a function value at a new point in two stages. The predictor step uses an explicit method to extrapolate an initial estimate of the function value at the new point, based on previously computed values and derivatives. The corrector step then refines that estimate using an implicit method that incorporates the predicted value, producing a more accurate result than either step could achieve alone. In practice, predictor-corrector methods typically pair an explicit method for the prediction with an implicit method for the correction, balancing computational cost against accuracy, and they are a standard tool wherever ordinary differential equations must be integrated numerically. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/