Abstract
In order to estimate local truncation errors of the Adams-Bashforth-Moulton pair of orderp (p=2, 3, 4, 5) in the mode of correcting to convergence, in theP(EC) m E mode and in theP(EC) m mode, we consider an accurate method by using a linear combination of the differences between the values of the predictor and those of the corrector. As one application, we also consider a method for estimating global truncation errors by using the estimated local truncation errors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S.O. Fatunla, Numerical Methods for Initial Value Problems in Ordinary Differential Equations. Academic Press, San Diego, 1985.
G. Hall and J.M. Watt, Modern Numerical Methods for Ordinary Differential Equations. Clarendon Press, Oxford, 1976.
R.W. Hamming, Numerical Methods for Scientists and Engineers. McGraw-Hill Book Company, New York, 1962.
P. Henrici, Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York, 1962.
J.D. Lambert, Computational Methods in Ordinary Differential Equations. Wiley, New York, 1973.
L. Lapidus and J.H. Seinfeld, Numerical Solution of Ordinary Differential Equations. Academic Press, New York, 1971.
L.F. Shampine and N.K. Gordon, Computer Solution of Ordinary Differential Equations, The Initial Value Problem. W.H. Freeman and Company, San Francisco, 1975.
H. Shintani, On errors in the numerical solutions of ordinary differential equations by step-by-step methods. Hiroshima Math. J.,10 (1980), 469–494.
Author information
Authors and Affiliations
About this article
Cite this article
Fujii, M. An extension of Milne's device for the Adams Predictor-Corrector Methods. Japan J. Indust. Appl. Math. 8, 1–18 (1991). https://doi.org/10.1007/BF03167183
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03167183