Chaos and Instability in Integration Algorithms Model DocumentsThis material has 2 associated documents. Select a document title to view a document's information. Main DocumentChaos and Instability in Integration Algorithms Model
written by
Fernando Silva Fernandes
The Chaos and Instability in Integration Algorithms Model uses the the nonlinear and nonautonomous differential equation dx/dt = t  x^2 to show how careful one must be when choosing a differential equation solver, even for an apparently simple problem. The chaotic behaviors here detected do not seem an intrinsic property of the differential equation, though the patterns are startling similar to the MayFeigenbaum's standard map. Indeed they disappear with more robust integration algorithms. The chaos here invoked only means that for some algorithms and integration times the trajectories are not random, but are unpredictable. Apparently, in such cases, there is also no dependence on initial conditions, a typical characteristic of intrinsic chaotic systems. This application illustrates that using an adaptive algorithm is not only a question of speed and CPU use, but also of precision and stability and the care that must be taken to avoid wrong conclusions, especially when using computer packages as "blackboxes."
Published September 1, 2014
This file has previous versions. Source Code DocumentsChaos and Instability in Integration Algorithms Source CodeThe source code zip archive contains an XML representation of the Chaos and Instability in Integration Algorithms Model. Unzip this archive in your EjsS workspace to compile and run this model using EjsS.
Last Modified September 1, 2014
