FAST SPECTRAL GALERKIN METHOD FOR LOGARITHMIC SINGULAR EQUATIONS ON A SEGMENT

Abstract

We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Convergence rates of several orders are obtained for fractional Sobolev spaces eH−1/2 (or H−1/2 00 ).
Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims.