The linear barycentric rational quadrature method for Volterra integral equations
- Berrut, Jean-Paul Department of Mathematics, University of Fribourg, Switzerland
- Hosseini, Seyyed Ahmad Department of Computer Sciences, Faculty of Sciences, Golestan University, Gorgan, Iran
- Klein, Georges Mathematical Institute, University of Oxford, UK
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01.01.2014
Published in:
- SIAM Journal on Scientific Computing. - 2014, vol. 36, no. 1, p. A105–A123
English
We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate as the rational quadrature rule but is costly on long integration intervals. The second, based on a composite version of this quadrature rule, loses one order of convergence but is much cheaper. Both require only a sample of the involved functions at equispaced nodes and yield an infinitely smooth solution of most classical examples with machine precision.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 210089
- DOI 10.1137/120904020
- Persistent URL
- https://folia.unifr.ch/unifr/documents/303647
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