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A fully discrete Galerkin method for Abel-type integral equations


Vögeli, Urs; Nedaiasl, Khadijeh; Sauter, Stefan A (2018). A fully discrete Galerkin method for Abel-type integral equations. Advances in Computational Mathematics:Epub ahead of print.

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.

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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Additional indexing

Item Type:Journal Article, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2018
Deposited On:28 Mar 2018 09:15
Last Modified:13 Apr 2018 11:49
ISSN:1019-7168
Additional Information:This is a post-peer-review, pre-copyedit version of an article published in Advances in computational mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10444-018-9598-4.
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s10444-018-9598-4

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Language: English
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Embargo till: 2019-03-12