Luisa Fermo

Luisa Fermo, Cornelis van der Mee, Sebastiano Seatzu

A numerical method to solve the direct scattering problem for the Zakharov-Shabat system associated to the initial value problem for the nonlinear Schroedinger equation is proposed. The method involves the numerical solution of Volterra integral systems with structured kernels and the identification of coefficients and parameters appearing in monomial-exponential sums. Numerical experiments confirm the effectiveness of the proposed technique.

Luisa Fermo, Valerio Loi

The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegö and anti-Szegö quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accuracy through their averaged results. Their computation involves a free parameter associated with the corresponding para-orthogonal polynomials. Here, it is suitably chosen to construct a Szegö and anti-Szegö formula whose nodes are strategically distanced from the singularity of the Hilbert kernel. Numerical experiments demonstrate the accuracy of the proposed method.