TY - JOUR
T1 - Fast Spectral Galerkin Method for Logarithmic Singular Equations on a Segment
AU - Jerez-Hanckes , Carlos
AU - Nicaise , Serge
AU - Urzúa-Torres , Carolina
JO - Journal of Computational Mathematics
VL - 1
SP - 128
EP - 158
PY - 2018
DA - 2018/02
SN - 36
DO - http://doi.org/10.4208/jcm.1612-m2016-0495
UR - https://global-sci.org/intro/article_detail/jcm/10586.html
KW - Screen problems, Boundary integral operators, Spectral methods.
AB - <p style="text-align: justify;">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 $\tilde{H}^{-1 ⁄ 2}$ (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.</p>