Numerical approximation of 2D Fredholm integral eigenvalue problems by orthogonal wavelets

摘要

We investigate the numerical approximation of two-dimensional, second kind Fredholm integral eigenvalue problems by the Galerkin method with the Cohen–Daubechies–Vial (CDV) wavelet family. This choice provides us orthogonal bases for bounded domains, avoiding the need of periodization or domain truncation. The CDV family is indexed by the number of vanishing moments, which drives the regularity of the basis. We generate the Galerkin basis from tensorized scaling functions and employ weighted Gaussian quadratures derived from refinement equations. Numerical experiments address the relative computational cost of this approach with respect to the Haar basis and the relationship between convergence rate and number of vanishing moments.