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Time Stepping Via One-Dimensional Padé Approximation

Amundsen, David E. and Bruno, Oscar (2007) Time Stepping Via One-Dimensional Padé Approximation. Journal of Scientific Computing, 30 (1). pp. 83-115. ISSN 0885-7474. https://resolver.caltech.edu/CaltechAUTHORS:20181105-143029068

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Abstract

The numerical solution of time-dependent ordinary and partial differential equations presents a number of well known difficulties—including, possibly, severe restrictions on time-step sizes for stability in explicit procedures, as well as need for solution of challenging, generally nonlinear systems of equations in implicit schemes. In this note we introduce a novel class of explicit methods based on use of one-dimensional Padé approximation. These schemes, which are as simple and inexpensive per time-step as other explicit algorithms, possess, in many cases, properties of stability similar to those offered by implicit approaches. We demonstrate the character of our schemes through application to notoriously stiff systems of ODEs and PDEs. In a number of important cases, use of these algorithms has resulted in orders-of-magnitude reductions in computing times over those required by leading approaches.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s10915-005-9021-4DOIArticle
https://rdcu.be/baN1aPublisherFree ReadCube access
ORCID:
AuthorORCID
Bruno, Oscar0000-0001-8369-3014
Additional Information:© 2005 Springer Science+Business Media, Inc. Received August 11, 2005; accepted (in revised form) October 14, 2005; Published online December 28, 2005. The authors wish to acknowledge useful conversations with Mike Giles, Jan Hesthaven and Lee Lindblom, whose independent tests of the PTS method gave rise important insights on the algorithm. DEA gratefully acknowledges support from NSERC Discovery Grant 249732-02 and Canada Foundation for Innovation New Opportunities Grant 7361. OB thankfully acknowledges support from the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant numbers F49620-99-1-0010 and F49620-02-1-0049, and from the NSF under contracts number DMS-9816802 and DMS-0104531. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)249732-02
Canada Foundation for Innovation7361
Air Force Office of Scientific Research (AFOSR)F49620-99-1-0010
Air Force Office of Scientific Research (AFOSR)F49620-02-1-0049
NSFDMS-9816802
NSFDMS-0104531
Subject Keywords:Numerical solution; explicit methods; evolution partial differential equations; stiff ordinary differential equations; Padé time stepping (PTS)
Issue or Number:1
Record Number:CaltechAUTHORS:20181105-143029068
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181105-143029068
Official Citation:Amundsen, D.E. & Bruno, O. J Sci Comput (2007) 30: 83. https://doi.org/10.1007/s10915-005-9021-4
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90649
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Nov 2018 18:29
Last Modified:03 Oct 2019 20:27

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