Two-step error estimators for implicit Runge--Kutta methods applied to stiff systems

This paper is concerned with local error estimation in the numerical integration of stiff systems of ordinary differential equations by means of Runge--Kutta methods. With implicit Runge--Kutta methods it is often difficult to embed a local error estimate with the appropriate order and stability pro...

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Bibliographic Details
Published in:ACM transactions on mathematical software 2004-03, Vol.30 (1), p.1-18
Main Authors: González--Pinto, S., Montijano, J. I., Pérez--Rodríguez, S.
Format: Article
Language:English
Subjects:
Error analysis
Estimates
Mathematical analysis
Ordinary differential equations
Studies
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Summary:This paper is concerned with local error estimation in the numerical integration of stiff systems of ordinary differential equations by means of Runge--Kutta methods. With implicit Runge--Kutta methods it is often difficult to embed a local error estimate with the appropriate order and stability properties. In this paper local error estimation based on the information from the last two integration steps (that are supposed to have the same steplength) is proposed. It is shown that this technique, applied to Radau IIA methods, lets us get estimators with proper order and stability properties. Numerical examples showing that the proposed estimate improves the efficiency of the integration codes are presented.
ISSN:0098-3500
1557-7295
DOI:10.1145/974781.974782