Predictor-Corrector Methods

A general set of methods for integrating ordinary differential equations. Predictor-corrector methods proceed by extrapolating a polynomial fit to the derivative from the previous points to the new point (the predictor step), then using this to interpolate the derivative (the corrector step). Press et al. (1992) opine that predictor-corrector methods have been largely supplanted by the Bulirsch-Stoer and Runge-Kutta methods, but predictor-corrector schemes are still in common use.

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 896-897, 1972.

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 493-494, 1985.

Mehrotra, S. "On the Implementation of a Primal-Dual Interior Point Method." SIAM J. Optimization 2, 575-601, 1992.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Multistep, Multivalue, and Predictor-Corrector Methods." §16.7 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 740-744, 1992.