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A Note on High/Low-Wave-Number Interactions in Spatially Discrete Parabolic Equations

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. http://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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https://doi.org/10.1093/imamat/42.1.27DOIArticle
https://academic.oup.com/imamat/article-abstract/42/1/27/872998/A-Note-on-High-Low-Wave-Number-Interactions-in?redirectedFrom=fulltextPublisherArticle
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.
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ10
Record Number:CaltechAUTHORS:20170613-135127282
Persistent URL:http://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:22 Aug 2017 20:59

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