In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation.
All such algorithms proceed in two steps: When considering the numerical solution of ordinary differential equations (ODEs), a predictor–corrector method typically uses an explicit method for the predictor step and an implicit method for the corrector step.
Consider the differential equation and denote the step size by
The Predict–Evaluate–Correct–Evaluate (PECE) mode refers to the variant in the above example: It is also possible to evaluate the function f only once per step by using the method in Predict–Evaluate–Correct (PEC) mode: Additionally, the corrector step can be repeated in the hope that this achieves an even better approximation to the true solution.
If the corrector method is iterated until it converges, this could be called PE(CE)∞.