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 ${\tilde {y}}_{2}$ by extrapolating to a future time $t_{2}$. Using the new value ${\tilde {y}}_{2}$ and its derivative there ${\tilde {y}}_{2}^{'}$ 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

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