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Analysis Still Matters: A Surprising Instance of Failure of Runge--Kutta--Felberg ODE Solvers

SIAM Rev. Volume 46, Issue 4, pp. 729-737 (2004)

Issue Date: 2004
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This paper provides a nice example to illustrate that without supporting analysis, a numerical simulation may lead to incorrect conclusions. We explore a pedagogical example of failure of Runge--Kutta--Felberg (RKF) algorithms for a simple dynamical system that models the coupling of two oscillators. Although the system appears to be well-behaved, the explicit RKF solvers provide erratic numerical solutions. The mode of failure is based in a period-doubling route to chaos due to the existence of stable linear solutions in the problem.

©2004 Society for Industrial and Applied Mathematics
Permalink: http://dx.doi.org/10.1137/S003614450342911X

KEYWORDS and AMS

Keywords
AMS Subject Classifications
37M99, 65L06, 65L20, 65P20, 97D40

PUBLICATION DATA

ISSN:
0036-1445 (print)   1095-7200 (online)
Publisher:
AIP is a member of CrossRef SIAM

REFERENCES (4)
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