Title: How to express the solution of an ODE as a linear system (in a suitable algebra) and exploit it for fast computation., Speaker(s): Dr Stefano Pozza, Charles University, Date and time: Feb 13, 2024, 3:00 PM (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Mancini). Address:
P.za dei Cavalieri, 7, 56126 Pisa PI
You can access the full event here: https://events.dm.unipi.it/e/254
Abstract --------
The solution of systems of non-autonomous linear ordinary differential equations is crucial in various applications, such as nuclear magnetic resonance spectroscopy. We introduced a new solution expression in terms of a generalization of the Volterra composition. Such an expression is linear in a particular algebraic structure of distributions, which can be mapped onto a subalgebra of infinite matrices. It is possible to exploit the new expression to devise fast numerical methods for linear non-autonomous ODEs. As a first example, we present a new method for the operator solution of the generalized Rosen-Zener model, a system of linear non-autonomous ODEs from quantum mechanics. The new method’s computing time scales linearly with the model’s size in the numerical experiments.
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