Virtual Seminar - Fruzsina Agocs

Wednesday Nov 11, 2020, 10:00 AM → 11:30 AM America/New_York

Title: (py)oscode: fast solutions of oscillatory ODEs in physics

Abstract: I will present (py)oscode, a Python/C++ package for efficiently solving
a class of highly oscillatory ordinary differential equations.

These type of equations occur frequently in physics, cosmology and
beyond, arising in quantum mechanics, electrical circuits, suspension
systems, molecular dynamics, and the extremely early universe. The
numerical solution of such systems is often the bottleneck in the
forward-modelling phase of Bayesian inference.

Even if the terms in the equation change slowly, if the frequency of
oscillations in the solution is high enough, standard numerical methods
struggle to solve such equations quickly. Traditional methods have to
trace every oscillation in the solution, taking many time-steps at an
enormous computational cost. The algorithm underlying pyoscode can
detect when the solution is oscillatory and switch to a method based on
an analytic approximation (called Wentzel-Kramers-Brillouin, WKB) suited
for oscillatory functions, otherwise using a conventional (Runge-Kutta,
RK) method. This allows the algorithm to skip over several wavelengths
of oscillation in a single step, reducing the number of time-steps taken
drastically.

In this talk, I will briefly summarise the algorithm underlying
pyoscode, show how it can be used as a general-purpose numerical ODE
solver, and present a range of physical applications, such as solving
for the energies of a quantum system and the rapid computation of
primordial power spectra for exploring models of cosmic inflation. I
will compare pyoscode's performance with popular available tools, and
discuss how pyoscode can be extended.

Please email Sara Mejias Gonzalez or Cindy Rampersad for Zoom information if you would like to participate.