Product quasi-interpolation in logarithmically singular integral equations
A discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of...
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Vilnius Gediminas Technical University
2012-11-01
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doaj-7213cc2db93848c59f9a828364fd9e932021-07-02T16:44:16ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102012-11-0117510.3846/13926292.2012.736089Product quasi-interpolation in logarithmically singular integral equationsEero Vainikko0Gennadi Vainikko1University of Tartu, Faculty of Mathematics and Computer Science Liivi 2, 50409 Tartu, EstoniaUniversity of Tartu, Faculty of Mathematics and Computer Science Liivi 2, 50409 Tartu, Estonia; Estonian Academy of Sciences Kohtu 6, 10130 Tallinn, Estonia A discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of variables, and on the product integration using quasi-interpolation by smooth splines of order m. Properties of different proposed calculation schemes are compared through numerical experiments using, in particular, variable precision interval arithmetics. https://journals.vgtu.lt/index.php/MMA/article/view/4904weakly singular integral equationsboundary singularitiesspline quasi-interpolationproduct integrationNyström-type methods |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Eero Vainikko Gennadi Vainikko |
spellingShingle |
Eero Vainikko Gennadi Vainikko Product quasi-interpolation in logarithmically singular integral equations Mathematical Modelling and Analysis weakly singular integral equations boundary singularities spline quasi-interpolation product integration Nyström-type methods |
author_facet |
Eero Vainikko Gennadi Vainikko |
author_sort |
Eero Vainikko |
title |
Product quasi-interpolation in logarithmically singular integral equations |
title_short |
Product quasi-interpolation in logarithmically singular integral equations |
title_full |
Product quasi-interpolation in logarithmically singular integral equations |
title_fullStr |
Product quasi-interpolation in logarithmically singular integral equations |
title_full_unstemmed |
Product quasi-interpolation in logarithmically singular integral equations |
title_sort |
product quasi-interpolation in logarithmically singular integral equations |
publisher |
Vilnius Gediminas Technical University |
series |
Mathematical Modelling and Analysis |
issn |
1392-6292 1648-3510 |
publishDate |
2012-11-01 |
description |
A discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of variables, and on the product integration using quasi-interpolation by smooth splines of order m. Properties of different proposed calculation schemes are compared through numerical experiments using, in particular, variable precision interval arithmetics.
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topic |
weakly singular integral equations boundary singularities spline quasi-interpolation product integration Nyström-type methods |
url |
https://journals.vgtu.lt/index.php/MMA/article/view/4904 |
work_keys_str_mv |
AT eerovainikko productquasiinterpolationinlogarithmicallysingularintegralequations AT gennadivainikko productquasiinterpolationinlogarithmicallysingularintegralequations |
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1721326244923965440 |