How to express the solution of an ODE as a linear system (in a suitable algebra) and exploit it for fast computation.

by Dr Stefano Pozza (Charles University)

Tuesday 13 Feb 2024, 15:00 → 16:00 Europe/Rome

Aula Mancini (Scuola Normale Superiore)

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.