Skip Navigation

IMA Journal of Numerical Analysis 2001 21(1):421-438; doi:10.1093/imanum/21.1.421
© 2001 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Van Den Heuvel, E. G.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Using resolvent conditions to obtain new stability results for {theta}-methods for delay differential equations

E. G. Van Den Heuvel1

1 Department of Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands, e-mail: heuvel{at}math.leidenuniv.nl

By using the Kreiss resolvent condition we establish upper bounds for the growth of errors in two simple, but typical, numerical processes for solving delay differential equations. We show that, when the {theta}-methods are used, with a suitably restricted stepsize, for solving the linear test problems Z'(t) = {lambda}Z(t) + µZ(t – {tau}), errors grow at most linearly with the number of timesteps and with the dimension involved. Moreover, we investigate whether this kind of error growth is valid uniformly within the so-called stability regions of these methods. Finally some numerical experiments are carried out with a representative member of the class of processes under consideration, and it is shown that our theoretical bounds for the error growth are of practical interest.

Received 9 March 1998. Accepted 5 January 1999.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.