Year: 2018
Author: Carlos Jerez-Hanckes, Serge Nicaise, Carolina Urzúa-Torres
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 1 : pp. 128–158
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 $\tilde{H}^{-1 ⁄ 2}$ (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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1612-m2016-0495
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 1 : pp. 128–158
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Screen problems Boundary integral operators Spectral methods.