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Predictor–corrector method
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<p>In <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>, predictor–corrector methods belong to a class of <a href="/facts/Algorithm/fnl5NmRt">algorithms</a> designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps: </p> <ol><li>The initial, "prediction" step, starts from a function fitted to the function-values and derivative-values at a preceding set of points to extrapolate ("anticipate") this function's value at a subsequent, new point.</li> <li>The next, "corrector" step refines the initial approximation by using the <i>predicted</i> value of the function and <i>another method</i> to interpolate that unknown function's value at the same subsequent point.</li></ol>