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Chaos and Instability in Integration Algorithms Model
written by Fernando Silva Fernandes
The Chaos and Instability in Integration Algorithms Model uses the the nonlinear and non-autonomous 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 May-Feigenbaum'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 "black-boxes."

The Chaos and Instability in Integration Algorithms Model was developed using version 5 of the Easy Java/JavaScript Simulations (EjsS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.   Double clicking the jar file will run the program if Java is installed.  You can modify this simulation if you have EjsS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

Please note that this resource requires at least version 1.7 of Java (JRE).
1 source code document is available
Subjects Levels Resource Types
General Physics
- Computational Physics
Mathematical Tools
- Numerical Analysis
Thermo & Stat Mech
- General
- Upper Undergraduate
- Lower Undergraduate
- Instructional Material
= Simulation
Intended Users Formats Ratings
- Learners
- Educators
- application/java
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Access Rights:
Free access
License:
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Fernando Silva Fernandes
Record Cloner:
Metadata instance created September 1, 2014 by Wolfgang Christian
Record Updated:
September 2, 2014 by Wolfgang Christian
Last Update
when Cataloged:
September 1, 2014
Other Collections:

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Record Link
AIP Format
F. Fernandes, Computer Program CHAOS AND INSTABILITY IN INTEGRATION ALGORITHMS MODEL (2014), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13340&DocID=3906).
AJP/PRST-PER
F. Fernandes, Computer Program CHAOS AND INSTABILITY IN INTEGRATION ALGORITHMS MODEL (2014), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13340&DocID=3906>.
APA Format
Fernandes, F. (2014). Chaos and Instability in Integration Algorithms Model [Computer software]. Retrieved December 18, 2017, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13340&DocID=3906
Chicago Format
Fernandes, Fernando Silva. "Chaos and Instability in Integration Algorithms Model." https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13340&DocID=3906 (accessed 18 December 2017).
MLA Format
Fernandes, Fernando Silva. Chaos and Instability in Integration Algorithms Model. Computer software. 2014. Java (JRE) 1.7. 18 Dec. 2017 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13340&DocID=3906>.
BibTeX Export Format
@misc{ Author = "Fernando Silva Fernandes", Title = {Chaos and Instability in Integration Algorithms Model}, Month = {September}, Year = {2014} }
Refer Export Format

%A Fernando Silva Fernandes
%T Chaos and Instability in Integration Algorithms Model
%D September 1, 2014
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13340&DocID=3906
%O application/java

EndNote Export Format

%0 Computer Program
%A Fernandes, Fernando Silva
%D September 1, 2014
%T Chaos and Instability in Integration Algorithms Model
%8 September 1, 2014
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13340&DocID=3906


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Chaos and Instability in Integration Algorithms Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Chaos and Instability in Integration Algorithms Model.

relation by Wolfgang Christian

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