(untitled) (Journal of Computational Mathematics, 2018)
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 H^-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 L^2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims.