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Stability, consistency and convergence of variable K-step methods for numerical integration of large systems of ordinary differential equations

  • Peter Piotrowski
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 109)

Abstract

This paper describes a generalization of the Adams method for systems of ordinary differential equations from constant to variable step sizes. This entailed deriving integration formulae and proving the stability, consistency, and convergence of their solutions.

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References

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    Henrici, Peter: Discrete variable methods in ordinary differential equations, John Wiley & Sons, INC, New York, London, Sydny 1962zbMATHGoogle Scholar
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    Henrici, Peter: Error propagation for difference methods, John Wiley & Sons, Inc. New York, London, Sydney 1963zbMATHGoogle Scholar
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    Collatz, L.: The numerical treatment of differential equations, Springer-Verlag, New York 1960CrossRefzbMATHGoogle Scholar
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    v. Hoerner, S.: Die numerische Integration des N-Körper-Problems für Sternhaufen I, Zeitschrift für Astrophysik 50, 184 (1960)zbMATHGoogle Scholar
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    Schlüter, A. and Piotrowski, P.: Numerical integration of large systems of ordinary differential equations by means of individually variable step size, Sonderheft der GAMM zur Jahrestagung 1968 in PragGoogle Scholar
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    Krogh, Fred T.: A variable step variable order multistep method for the numerical solution of ordinary differential equations, IFIP Congress 1968, booklet A 91–95Google Scholar
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    referred to and applied by Aarseth, S. J.: Dynamical evolution of clusters of galaxis, M. N. 126, 223 (1963)Google Scholar

Copyright information

© Springer-Verlag 1969

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  • Peter Piotrowski

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