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. doi:10.1007/s10208001002. 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.
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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. | ||||||||||||
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Issue or Number: | 1 | ||||||||||||
Classification Code: | AMS Classification. 34A65, 60H10, 65L70, 82C80 | ||||||||||||
DOI: | 10.1007/s10208001002 | ||||||||||||
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: | 15 Nov 2021 17:37 |
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