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A numerical study of chaos in a reaction‐diffusion equation
Author(s) -
Mitchell A. R.,
Bruch J. C.
Publication year - 1985
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690010104
Subject(s) - discretization , mathematics , chaotic , aperiodic graph , chaos (operating system) , euler's formula , diffusion , reaction–diffusion system , nonlinear system , backward euler method , euler equations , series (stratigraphy) , numerical analysis , mathematical analysis , computer science , physics , thermodynamics , paleontology , computer security , combinatorics , quantum mechanics , artificial intelligence , biology
A study is made using numerical experiments to see the effect of the parameters in the explicit Euler‐discretized form of a one‐dimensional, nonlinear, reaction‐diffusion equation. Based on a series of these experiments, one of the main results obtained is that diffusion, which is usually perceived as having a stabilizing effect, is able to produce chaotic as well as divergent numerical solutions. Furthermore, the discretization parameters are also able to produce chaotic results. From the results presented herein, it is shown that varying the parameters can produce solutions that are single numbers, periodic, aperiodic (chaos), or divergent.