Stuart, Andrew (1989) A Note on High/Low-Wave-Number Interactions in Spatially Discrete Parabolic Equations. IMA Journal of Applied Mathematics, 42 (1). pp. 27-42. ISSN 0272-4960. doi:10.1093/imamat/42.1.27. https://resolver.caltech.edu/CaltechAUTHORS:20170613-135127282
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Abstract
We describe an instability introduced by the spatial discretization of reaction-diffusion equations. The mechanism is a nonlinear interaction between high and low wave-number modes in the discrete equations. In partial differential equations which exhibit strong temporal growth, a parasitic high-wave-number mode is stimulated, through aliasing, by a physically meaningful low-wave-number mode. We analyse the interaction using phase-plane techniques and present complementary numerical results.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1989 Oxford University Press. Published: 01 January 1989. Received: 30 June 1988. I am grateful to both referees for suggestions which improved the presentation of this material. | |||||||||
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| Issue or Number: | 1 | |||||||||
| DOI: | 10.1093/imamat/42.1.27 | |||||||||
| Record Number: | CaltechAUTHORS:20170613-135127282 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170613-135127282 | |||||||||
| Official Citation: | ANDREW STUART; A Note on High/Low-Wave-Number Interactions in Spatially Discrete Parabolic Equations. IMA J Appl Math 1989; 42 (1): 27-42. doi: 10.1093/imamat/42.1.27 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 78171 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 13 Jun 2017 21:02 | |||||||||
| Last Modified: | 15 Nov 2021 17:37 |
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