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The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations

Hagstrom, Thomas and Keller, H. B. (1986) The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations. SIAM Journal of Scientific and Statistical Computing, 7 (3). pp. 978-988. ISSN 0196-5204. doi:10.1137/0907065.

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Traveling wave solutions have been studied for a variety of nonlinear parabolic problems. In the initial value approach to such problems the initial data at infinity determines the wave that propagates. The numerical simulation of such problems is thus quite difficult. If the domain is replaced by a finite one, to facilitate numerical computations, then appropriate boundary conditions on the "artificial" boundaries must depend upon the initial data in the discarded region. In this work we derive such boundary conditions, based on the Laplace transform of the linearized problems at ±∞, and illustrate their utility by presenting a numerical solution of Fisher’s equation which has been proposed as a model in genetics.

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Additional Information:© 1986 Society for Industrial and Applied Mathematics. Received by the editors May 24, 1984, and in revised form July 1, 1985. This research was sponsored in part by the U.S. Department of Energy under contract DE-AS03-76SF-00767, and by the U.S. Army under contract DAAG29-80-C-0041. The authors thank Prof. J.D. Murray for bringing this problem to our attention.
Funding AgencyGrant Number
Department of Energy (DOE)DE-AS03-76SF-00767
Army Research Office (ARO)DAAG29-80-C-0041
Subject Keywords:artificial boundary conditions; parabolic traveling waves
Issue or Number:3
Record Number:CaltechAUTHORS:HAGsiamjssc86
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13078
Deposited On:02 Feb 2009 22:24
Last Modified:08 Nov 2021 22:35

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