Fast spectral Galerkin method for logarithmic singular equations on a segment

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 He −1/2 (or H00 1/2). Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims.

Original languageEnglish
Pages (from-to)128-158
Number of pages31
JournalJournal of Computational Mathematics
Volume36
Issue number1
DOIs
StatePublished - 2019
Externally publishedYes

Keywords

  • Boundary integral operators
  • Screen problems
  • Spectral methods

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