The Taylor Center ODEs Solver as a Generator of Simulations
0Presented by:
Alexander Gofen, The Taylor Center, San Francisco CA USA
https://qubeshub.org/community/groups/simiode/expo
Abstract: First, the only goal of this All-in-One Taylor integrator [1] for challenging ODEs was scientific research and numeric experimentation [2, 3].
Later, I began collecting illustrious problems in applied ODEs—now a vast list [4] of simulations (without textbooks indeed).
Yet the very method of the real-time graphics suggested to utilize it as a generator of simulations or a virtual lab (Exploratorium [5]). Now it consists of only a few topics in my own expertise: didactic texts with directives what to watch in the respective simulations. When readers encounter a name of a simulation, there is a mechanism for running it by selecting its name.
In fact, any textbook for applied ODEs may be enriched with such simulations. Consequently, instead of still images, the textbook will provide a live real-time animation. And this is the main message of my talk today, and of the Workshop [6].
1. The software. http://TaylorCenter.org/Gofen/TaylorMethod.htm
2. R. Montgomery. Dropping bodies. The Mathematical Intelligencer. 2023. https://link.springer.com/content/pdf/10.1007/s00283-022-10252-4.pdf
3. M. Frenkel et al. The Continuous Measure of Symmetry as a Dynamic Variable. Symmetry. 2023, 15, 2153. https://doi.org/10.3390/sym15122153
4. Simulations (though without textbooks), http://TaylorCenter.org/Gofen/Teaching/Samples.htm
5. Exploratorium, i.e. textbooks with the respective simulations, http://TaylorCenter.org/Exploratorium
6. The Workshop, http://TaylorCenter.org/Workshops.htm