The current research of the Numerical Analysis Group (Department of Mathematics and Computer Science) focuses on the following main topics:
Interpolation and approximation of scatterd data
Our contribution in this direction consists in the construction of Shepard’s like methods (combined Shepard methods, triangular and hexagonal Shepard methods) which improve in accuracy and behaviour the Shepard’s one.
Global methods for the solution of Initial Value Problems or Boundary Value Problems for Ordinary Differential Equations.
The reseach on this topic focuses on the use of special polynomial basis for the definition of spectral methods, and more precisely collocation methods.
The research focuses, essentially, on the Umbral Calculus, with the development of a an approach, different from the Rota’s one, that allows to deduce both known results in simpler way and new characterizations and algorithms.