17-09-2024
The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Analysis with the title: “Nyström methods for Fredholm integral equations defined on planar domains”. Maria Grazia Russo (Department of Engineering, University of Basilicata, Italy) is the speaker.
Abstract: The talk is devoted to a general Nyström scheme for approximating bivariate linear integral equations of the second kind defined on suitable domains of the plane.
The basic idea of the numerical strategy is to use a global approach, that is to use cubature rules built starting from a polynomial approximation scheme.
In fact, the global approximation allows to obtain excellent convergence results, since the order of convergence of the corresponding Nyström methods, is
the same as the best polynomial approximation of the solution in suitable selected spaces of functions. Furthermore, in this context it is quite easy to prove the
stability of the methods and the good conditioning of the involved linear systems.
We will give an overview of several results obtained in the last few years, starting from rectangular bounded or unbounded domains, also in the case
where the known functions of the equation may have singularities on the boundaries, and arriving at the case of equations defined on curvilinear domains.
Wednesday, 25 September 2024, from 14:15 to 15:15.
