On the Numerical Integration of Ordinary Differential Equations by Processed Methods

We provide a theoretical analysis of the processing technique for the numerical integration of ODEs. We get the effective order conditions for processed methods in a general setting so that the results obtained can be applied to different types of numerical integrators. We also propose a procedure t...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2004-01, Vol.42 (2), p.531-552
Main Authors: Blanes, S., Casas, F., Murua, A.
Format: Article
Language:English
Subjects:
Methods
Ordinary differential equations
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Summary:We provide a theoretical analysis of the processing technique for the numerical integration of ODEs. We get the effective order conditions for processed methods in a general setting so that the results obtained can be applied to different types of numerical integrators. We also propose a procedure to approximate the postprocessor such that its evaluation is virtually cost-free. The analysis is illustrated for a particular class of composition methods.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142902417029