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On spurious steady-state solutions of explicit Runge-Kutta schemesThe 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.
Document ID
19900013024
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Sweby, P. K. (Reading Univ. (England). Moffett Field, CA., United States)
Yee, H. C. (NASA Ames Research Center)
Griffiths, D. F. (Dundee Univ.)
Date Acquired
September 6, 2013
Publication Date
April 1, 1990
Subject Category
Numerical Analysis
Report/Patent Number
NAS 1.15:102819
A-90148
NASA-TM-102819
Meeting Information
Meeting: International Conference on Hyperbolic Problems
Location: Uppsala
Country: Sweden
Start Date: June 11, 1990
End Date: June 15, 1990
Accession Number
90N22340
Funding Number(s)
PROJECT: RTOP 505-60-00
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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