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10–48.Wanner, G. 1988, in Numerical Analysis 1987, Pitman Research Notes in Mathematics, vol. 170,D.F. Griffiths and G.A. Watson, eds. (Harlow, Essex, U.K.: Longman Scientific and Technical).Stoer, J., and Bulirsch, R. 1980, Introduction to Numerical Analysis (New York: Springer-Verlag).16.7 Multistep, Multivalue, andPredictor-Corrector MethodsThe terms multistep and multivalue describe two different ways of implementingessentially the same integration technique for ODEs. Predictor-corrector is a particular subcategrory of these methods — in fact, the most widely used. Accordingly,the name predictor-corrector is often loosely used to denote all these methods.We suspect that predictor-corrector integrators have had their day, and that theyare no longer the method of choice for most problems in ODEs.
For high-precisionapplications, or applications where evaluations of the right-hand sides are expensive,Bulirsch-Stoer dominates. For convenience, or for low precision, adaptive-stepsizeRunge-Kutta dominates. Predictor-corrector methods have been, we think, squeezedSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use.
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