@Article{JCM-36-1,
author = {Jerez-Hanckes, Carlos and Serge, Nicaise and Urzúa-Torres, Carolina},
title = {Fast Spectral Galerkin Method for Logarithmic Singular Equations on a Segment},
journal = {Journal of Computational Mathematics},
year = {2018},
volume = {36},
number = {1},
pages = {128--158},
abstract = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1612-m2016-0495},
url = {https://global-sci.com/article/84461/fast-spectral-galerkin-method-for-logarithmic-singular-equations-on-a-segment}
}