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Volume 36, Issue 1
Fast Spectral Galerkin Method for Logarithmic Singular Equations on a Segment

Carlos Jerez-Hanckes, Serge Nicaise & Carolina Urzúa-Torres

DOI: 10.4208/jcm.1612-m2016-0495

J. Comp. Math., 36 (2018), pp. 128-158.

Published online: 2018-02

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  • 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.

  • Keywords

Screen problems, Boundary integral operators, Spectral methods.

  • AMS Subject Headings

65R20, 65F35, 65N22, 65N38.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

cjerez@ing.puc.cl (Carlos Jerez-Hanckes)

serge.nicaise@univ-valenciennes.fr (Serge Nicaise)

carolina.urzua@sam.math.ethz.ch (Carolina Urzúa-Torres)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-128, author = {Jerez-Hanckes , CarlosNicaise , Serge 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 = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1612-m2016-0495}, url = {http://global-sci.org/intro/article_detail/jcm/10586.html} }
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 -

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.

Jerez-Hanckes , CarlosNicaise , Serge and Urzúa-Torres , Carolina. (2018). Fast Spectral Galerkin Method for Logarithmic Singular Equations on a Segment. Journal of Computational Mathematics. 36 (1). 128-158. doi:10.4208/jcm.1612-m2016-0495
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