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The asymptotic discretization error of a class of methods for solving ordinary differential equations

Published online by Cambridge University Press:  24 October 2008

J. M. Watt
J. M. Watt
Affiliation:
Subdepartment of Numerical Analysis, The University, Liverpool 3*
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Abstract

The order and asymptotic form of the error of a general class of numerical method for solving the initial value problem for systems of ordinary differential equations is considered. Previously only the convergence of the methods, which include Runge-Kutta and linear multistep methods, has been discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 461 - 472
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Butcher, J. C.A modified multistep method for the numerical integration of ordinary differential equations. J. Assoc. Comput. Mach. 12 (1965), 124–135.CrossRefGoogle Scholar
(2)Butcher, J. C.On the convergence of numerical solutions to ordinary differential equations. Math. Comp. 20 (1966), 1–10.CrossRefGoogle Scholar
(3)Dieudonné, J.Foundations of modern analysis (Academic Press; New York and London, 1960).Google Scholar
(4)Gear, C. W.Hybrid methods for initial value problems in ordinary differential equations. J. Soc. Indust. Appl. Math. Ser. B. Numer. Anal. 2 (1965), 69–86.CrossRefGoogle Scholar
(5)Gragg, W. G. and Stetter, H. J.Generalised multistep predictor-corrector methods. J. Assoc. Comput. Mach. 11 (1964), 188–209.CrossRefGoogle Scholar
(6)Henrici, P.Discrete variable methods in ordinary differential equations (Wiley; New York, 1962).Google Scholar
(7)Henrici, P.Error propagation for difference methods (Wiley; New York, 1963).Google Scholar
(8)Kolmogorov, A. A. and Fomin, S. V.Elements of the theory of functions and functional analysis (Graylock Press; Rochester N.Y., 1957).Google Scholar
(9)Liusternik, L. A. and Sobolev, V. J.Elements of functional analysis (Ungar; New York, 1961).Google Scholar
(10)Spijker, M. N.Convergence and stability of step-by-step methods for the numerical solution of initial value problems. Numer. Math. 8 (1966), 161–177.CrossRefGoogle Scholar