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Linear Instability Implies Spurious Periodic Solutions

Stuart, Andrew (1989) Linear Instability Implies Spurious Periodic Solutions. IMA Journal of Numerical Analysis, 9 (4). pp. 465-486. ISSN 0272-4979. doi:10.1093/imanum/9.4.465.

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We analyse discrete approximations of reaction-diffusion-convection equations and show that linearized instability implies the existence of spurious periodic solutions in the fully nonlinear problem. The result is proved by using ideas from bifurcation theory. Using singularity theory we provide a precise local description of the spurious solutions. The results form the basis for an analysis of the range of discretization parameters in which spurious solutions can exist, their magnitude, and their spatial structure. We present a modified equations approach to determine criteria under which spurious periodic solutions exist for arbitrarily small values of the time-step. The theoretical results are applied to a specific example.

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Additional Information:© 1989 Oxford University Press. Received 20 November 1988. Revision Received: 20 March 1989. Most of this work was carried out at the Department of Mathematics, Massachusetts Institute of Technology.
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ12
Issue or Number:4
Record Number:CaltechAUTHORS:20170612-083455306
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Official Citation:ANDREW STUART; Linear Instability Implies Spurious Periodic Solutions. IMA J Numer Anal 1989; 9 (4): 465-486. doi: 10.1093/imanum/9.4.465
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78087
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2017 16:05
Last Modified:15 Nov 2021 17:36

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