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Fast Spectral Galerkin Method for Logarithmic Singular Equations on a Segment

Fast Spectral Galerkin Method for Logarithmic Singular Equations on a Segment
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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.

Author Details

Carlos Jerez-Hanckes

Serge Nicaise

Carolina Urzúa-Torres

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