Dajana CONTE | Seminari Laboratorio di Analisi Numerica 11/05/2023

Giovedì 11 maggio alle ore 10 nella sala riunioni del Dipartimento di Matematica, Il prof. Teo Roldan, professore associato presso l’Università Pubblica di Navarra (Spagna), terrà un seminario dal titolo:

Positivity and Contractivity of Crank-Nicolson Method

ABSTRACT

In this talk we deal with qualitative properties of Crank-Nicolson method when it is applied to the diffusion equation. We consider both Dirichlet and Periodic boundary conditions. In each case we get necessary and sufficient conditions for positivity and contractivity, where the contractivity bounds have been obtained for the maximum norm. The analysis has been done by using a kind of Chebyshev-like polynomials.

The bounds for positivity and contractivity have been obtained for any value of the space discretization parameter m. In the limit, when m tends to infinity, we recover some know results. These ideas can be extended for other time integrator methods like for example theta-methods.

Pubblicato il 1 Maggio 2023 da CONTE Dajana