Anti-Gauss cubature rules with applications to Fredholm integral equations on the square
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909603150692352 |
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| author | de Alba, Patricia Diaz Fermo, Luisa Rodriguez, Giuseppe |
| author_facet | de Alba, Patricia Diaz Fermo, Luisa Rodriguez, Giuseppe |
| contents | The purpose of this paper is to develop the anti-Gauss cubature rule for approximating integrals defined on the square whose integrand function may have algebraic singularities at the boundaries. An application of such a rule to the numerical solution of Fredholm integral equations of the second-kind is also explored. The stability, convergence, and conditioning of the proposed Nyström-type method are studied. The numerical solution of the resulting dense linear system is also investigated and several numerical tests are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15967 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anti-Gauss cubature rules with applications to Fredholm integral equations on the square de Alba, Patricia Diaz Fermo, Luisa Rodriguez, Giuseppe Numerical Analysis 65R20, 65D30, 42C0 The purpose of this paper is to develop the anti-Gauss cubature rule for approximating integrals defined on the square whose integrand function may have algebraic singularities at the boundaries. An application of such a rule to the numerical solution of Fredholm integral equations of the second-kind is also explored. The stability, convergence, and conditioning of the proposed Nyström-type method are studied. The numerical solution of the resulting dense linear system is also investigated and several numerical tests are presented. |
| title | Anti-Gauss cubature rules with applications to Fredholm integral equations on the square |
| topic | Numerical Analysis 65R20, 65D30, 42C0 |
| url | https://arxiv.org/abs/2311.15967 |