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Friday, June 23 • 2:18pm - 2:54pm
TaylorIntegration.jl: Taylor's Integration Method in Julia

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In this talk we shall present TaylorIntegration.jl, an ODE integration package using Taylor's method in Julia. The main idea of Taylor's method is to approximate locally the solution by means by a high-order Taylor expansion, whose coefficients are computed recursively using automatic differentiation techniques. One of the principal advantages of Taylor's method is that, whenever high accuracy is required, the order of the method can be increased, which is more efficient computationally than taking smaller time steps. The accuracy of Taylor's method permits to have round-off errors per integration step. Traditionally, it has been difficult to make a generic Taylor integration package, but Julia permits this beautifully. We shall present some examples of the application of this method to ODE integration, including the whole computation of the Lyapunov spectrum, use of jet transport techniques, and parameter sensitivity. Open issues related to improving performance will be described.

avatar for Luis Benet

Luis Benet

I am a physicist interested in precise integrations of Solar System minor bodies. I am author of TaylorSeries.jl, TaylorIntegration.jl, TaylorModels.jl, and ValidatedNumerics.jl.

Jorge Antonio Pérez Hernández

PhD candidate, UNAM
Jorge Perez is a Physics Ph.D. student at UNAM, Mexico, under supervision of Luis Benet and David P. Sanders, authors of TaylorSeries.jl and ValidatedNumerics.jl. His Ph.D. research project is related to understanding the dynamics of minor Solar System objects: comets, asteroids... Read More →

Friday June 23, 2017 2:18pm - 2:54pm PDT
West Pauley Pauley Ballroom, Berkeley, CA