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 ${\displaystyle y_{0}}$  and ${\displaystyle y_{1}}$  at times ${\displaystyle t_{0}}$  and ${\displaystyle t_{1}}$ . By fitting a cubic polynomial to the points and their derivatives (gotten through the differential equation), one can predict a point ${\displaystyle {\tilde {y}}_{2}}$  by extrapolating to a future time ${\displaystyle t_{2}}$ . Using the new value ${\displaystyle {\tilde {y}}_{2}}$  and its derivative there ${\displaystyle {\tilde {y}}_{2}^{'}}$  along with the previous points and their derivatives, one can then better interpolate the derivative between ${\displaystyle t_{1}}$  and ${\displaystyle t_{2}}$  to get a better approximation ${\displaystyle y_{2}}$ . 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

• Weisstein, Eric W. "Predictor-Corrector Methods". MathWorld.
• Predictor-corrector methods for differential equations