Linear Multistep Methods and Order Stars: Some Properties

J.C. Ferreira, S.A. Meira, M. Meneguette Jr., J.R. Nogueira

Abstract


Order stars theory, introduced by Wanner et al (1978), have become a fundamental tool for understanding of order and stability properties of numerical methods. In this work we intend to study some properties of numerical linear multistep methods using this theory.

References


[1] L.V.Ahlfors, “Analisis de Variable Compleja”, Aguilar, Madrid, 1966.

J.B. Conway, “Functions of One Complex Variable”, Springer-Verlag, New York, 1978.

E. Hairer, G. Wanner, “Order Stars and Stiff Integrators”, Section de mathématiques CH-1211, Université de Genève, Switzerland, 1999.

P. Henrici, “Discrete Variable Methods in Ordinary Differential Equations”, John Wiley & Sons, New York, 1962.

P. Henrici, “Elements of Numerical Analysis”, John Wiley & Sons, New York,1964.

A. Iserles, S.P. Nørsett, “Order Stars”, Chapmam & Hall, London, 1991.

J.D. Lambert,“Computational Methods in Ordinary Differential Equations”, John Wiley & Sons, London, 1973.




DOI: https://doi.org/10.5540/tema.2008.09.02.0233

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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