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On spurious steady-state solutions of explicit Runge-Kutta schemes

Author
Sweby, P. K.
Published
Apr 1, 1990.
Physical Description
1 electronic document
Additional Creators
Griffiths, D. F. and Yee, H. C.
Online Version

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Summary
The bifurcation diagram associated with the logistic equation v sup n+1 = av sup n (1-v sup n) is by now well known, as is its equivalence to solving the ordinary differential equation u prime = alpha u (1-u) by the explicit Euler difference scheme. It has also been noted by Iserles that other popular difference schemes may not only exhibit period doubling and chaotic phenomena but also possess spurious fixed points. Runge-Kutta schemes applied to both the equation u prime = alpha u (1-u) and the cubic equation u prime = alpha u (1-u)(b-u) were studied computationally and analytically and their behavior was contrasted with the explicit Euler scheme. Their spurious fixed points and periodic orbits were noted. In particular, it was observed that these may appear below the linearized stability limits of the scheme and, consequently, computation may lead to erroneous results.
Other Subject(s)
Collection
NASA Technical Reports Server (NTRS) Collection.
Note
Document ID: 19900013024.
Accession ID: 90N22340.
A-90148.
NASA-TM-102819.
NAS 1.15:102819.
International Conference on Hyperbolic Problems; 11-15 Jun. 1990; Uppsala; Sweden.
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No Copyright.
View MARC record | catkey: 15686403