A fully discrete Galerkin method for Abel-type integral equations

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.

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Correspondence to Stefan A. Sauter.

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Communicated by: Leslie Greengard

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Vögeli, U., Nedaiasl, K. & Sauter, S.A. A fully discrete Galerkin method for Abel-type integral equations. Adv Comput Math 44, 1601–1626 (2018). https://doi.org/10.1007/s10444-018-9598-4

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Keywords

  • Abel’s integral equation
  • Galerkin method
  • Tensor-Gauss quadrature

Mathematics Subject Classification (2000)

  • 45E10
  • 65R20
  • 65D32