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Stiff Oscillatory Systems, Delta Jumps and White Noise

Cano, B. and Stuart, A. M. and Süli, E. and Warren, J. O. (2001) Stiff Oscillatory Systems, Delta Jumps and White Noise. Foundations of Computational Mathematics, 1 (1). pp. 69-100. ISSN 1615-3375. https://resolver.caltech.edu/CaltechAUTHORS:20170613-130016747

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Abstract

Two model problems for stiff oscillatory systems are introduced. Both comprise a linear superposition of N ≫ 1 harmonic oscillators used as a forcing term for a scalar ODE. In the first case the initial conditions are chosen so that the forcing term approximates a delta function as N → ∞ and in the second case so that it approximates white noise. In both cases the fastest natural frequency of the oscillators is <e6>OM</e6>(N). The model problems are integrated numerically in the stiff regime where the time-step Δt satisfies NΔt=O(1). The convergence of the algorithms is studied in this case in the limit N → ∞ and Δt → 0.For the white noise problem both strong and weak convergence are considered. Order reduction phenomena are observed numerically and proved theoretically.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s10208001002DOIArticle
https://link.springer.com/article/10.1007/s10208001002PublisherArticle
http://rdcu.be/trCGPublisherFree ReadCube access
Additional Information:© 2000 Society for the Foundation of Computational Mathematics. August 25, 1999. Final version received: May 3, 2000. B. Cano was supported by JCL VA36/98 and DGICYT PB95-705. A. M. Stuart was supported by the National Science Foundation under grant DMS-95-04879 and by the EPSRC under grant GR/L82922, and J. O. Warren was supported by the Department of Defense Science and Engineering Graduate Fellowship Program. We are grateful to a referee for suggesting inclusion of the material in Section 3.
Funders:
Funding AgencyGrant Number
JCLJCL VA36/98
Dirección General de Investigación Científica y Técnica (DGICYT)PB95-705
NSFDMS-95-04879
Engineering and Physical Sciences Research Council (EPSRC)GR/L82922
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ46
Issue or Number:1
Classification Code:AMS Classification. 34A65, 60H10, 65L70, 82C80
Record Number:CaltechAUTHORS:20170613-130016747
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170613-130016747
Official Citation:Cano, B., Stuart, A., Süli, E. et al. Found. Comput. Math. (2001) 1: 69. doi:10.1007/s10208001002
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78166
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 Jun 2017 20:18
Last Modified:03 Oct 2019 18:06

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