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Advances in Computational Mathematics

, Volume 44, Issue 5, pp 1601–1626 | Cite as

A fully discrete Galerkin method for Abel-type integral equations

  • Urs Vögeli
  • Khadijeh Nedaiasl
  • Stefan A. SauterEmail author
Article
  • 72 Downloads

Abstract

In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence estimates are derived in fractional-order Sobolev norms. The fully-discrete Galerkin method is defined by employing simple tensor-Gauss quadrature. We develop a corresponding perturbation analysis which allows to keep the number of quadrature points small. Numerical experiments have been performed which illustrate the sharpness of the theoretical estimates and the sensitivity of the solution with respect to some parameters in the equation.

Keywords

Abel’s integral equation Galerkin method Tensor-Gauss quadrature 

Mathematics Subject Classification (2000)

45E10 65R20 65D32 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland
  2. 2.Institute for Advanced Studies in Basic SciencesZanjanIran

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