C Foias et al 2002 Nonlinearity 15 1881 doi:10.1088/0951-7715/15/6/308
C Foias1,2, M S Jolly2 and W-S Li3,4
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A Nevanlinna–Pick algorithm is developed and applied to short numerical time series approximating trajectories of ordinary differential equations to determine whether the data are near the global attractor. The algorithm, while ultimately unstable to numerical error, is found to give reliable results for more data points than standard algorithms commonly used today. Connections between the growth of trajectories backward in time and the success in locating the global attractor are explored. The numerical sensitivity to both round-off errors and the integrator used to generate the time series is analysed. Applications are made to the Lorenz system and Kuramoto–Sivashinsky equation.
02.60.Lj Ordinary and partial differential equations; boundary value problems
34L30 Nonlinear ordinary differential operators
Issue 6 (November 2002)
Received 5 October 2001, in final form 16 June 2002
Published 23 September 2002
C Foias et al 2002 Nonlinearity 15 1881
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