Predictor-corrector method

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.

Example

In approximating the solution to a first-order ordinary differential equation, suppose one knows the solution points $y\_0$ and $y\_1$ at times $t\_0$ and $t\_1$. By fitting a cubic polynomial to the points and their derivatives (gotten through the differential equation), one can predict a point $ilde\{y\}\_2$ by extrapolating to a future time $t\_2$. Using the new value $ilde\{y\}\_2$ and its derivative there $ilde\{y\}^\text{'}\_2$ along with the previous points and their derivatives, one can then better interpolate the derivative between $t\_1$ and $t\_2$ to get a better approximation $y\_2$. The interpolation and subsequent integration of the differential equation constitute the corrector step.

See also

* Backward differentiation formula
* Beeman's algorithm
* Heun's method
* Mehrotra predictor-corrector method
* Numerical continuation

External links

*
* [http://www.fisica.uniud.it/~ercolessi/md/md/node22.html Predictor-corrector methods] for differential equations