Predictor–corrector method: Difference between revisions

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{{Short description|Algorithms in numerical analysis}}

In [[numerical analysis]], '''predictor–corrector methods''' belong to a class of [[algorithm]]s designed to integrate [[ordinary differential equation]]sequations{{snd}}to find an unknown [[function (mathematics)|function]] that satisfies a given [[differential equation]]. All such algorithms proceed in two steps:

# The initial, "prediction" step, starts from a function fitted to the function-values and [[derivative (mathematics)|derivative]]-values at a preceding set of points to extrapolate ("anticipate") this function's value at a subsequent, new point.

# The next, "corrector" step refines the initial approximation by using the ''predicted'' value of the function and ''another method'' to interpolate that unknown function's value at the '''same''' subsequent point.

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\end{align} </math>

The PECEC mode has one fewer function evaluation. than PECECE mode.

More generally, if the corrector is run ''k'' times, the method is in P(EC)^''k''

or P(EC)^''k''E mode. If the corrector method is iterated until it converges, this could be called PE(CE)^∞.<ref>{{harvnb|Butcher|2003|p=104}}</ref>

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* {{MathWorld |title=Predictor-Corrector Methods |urlname=Predictor-CorrectorMethods}}

* [https://web.archive.org/web/20080617035745/http://www.fisica.uniud.it/~ercolessi/md/md/node22.html Predictor–corrector methods] for differential equations

{{Numerical integrators}}

{{DEFAULTSORT:Predictor-corrector method}}