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Numerical Methods for Delay Differential Equations$
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Alfredo Bellen and Marino Zennaro

Print publication date: 2003

Print ISBN-13: 9780198506546

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198506546.001.0001

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Local Error Estimate and Variable Stepsize

Local Error Estimate and Variable Stepsize

Chapter:
(p.183) 7 Local Error Estimate and Variable Stepsize
Source:
Numerical Methods for Delay Differential Equations
Author(s):

Alfredo Bellen

Marino Zennaro

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198506546.003.0007

This chapter focuses on the stepsize control mechanism, which plays a central role in the production of efficient numerical codes for DDEs. In particular, the importance of the choice of the continuous extension in the estimation of the local error, and its influence on the response of the global error to the user supplied tolerance are discussed. The developed theory is applied to a sample advancing method of order four with error-estimating method of order five. First, the case of DDEs with non-vanishing delays is considered, and then the procedure is extended to DDEs with delays of arbitrary type, possibly vanishing at some points and/or even state-dependent. The implementation of the code RADAR5, introduced in Chapter 6, is illustrated based on two critical examples.

Keywords:   stepsize control, tolerance, local error, global error, advancing method, error-estimating method, code RADAR5

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