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Resumo:We consider the numerical approximation of homogeneous Fredholm integral equations of second kind. We employ the wavelet Galerkin method with 2D Haar wavelets as shape functions. We thoroughly describe the derivation of the shape functions and present a preliminary numerical experiment illustrating the computation of eigenvalues for a particular covariance kernel.Palavras-chave: Fredholm integral equations, Galerkin method, 2D Haar wavelets

We study the numerical evaluation of integrals involving scaling functions from the Cohen-Daubechies-Vial (CDV) family of compactly supported orthogonal wavelets on the interval. The computation of the wavelet coefficients is performed by a weighted Gaussian quadrature, in conjunction with the Chebyshev and modified Chebyshev algorithms. We validate the proposed quadratures with the numerical approximation of a Fredholm integral equation of second kind by the Galerkin method with CDV scaling functions as basis functions.