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arXiv · 2311.15967

Anti-Gauss cubature rules with applications to Fredholm integral equations on the square

Patricia Diaz de Alba·Luisa Fermo·Giuseppe Rodriguez
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Abstract

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 Nystr\"om-type method are studied. The numerical solution of the resulting dense linear system is also investigated and several numerical tests are presented.

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Patricia Diaz de Alba, Luisa Fermo, Giuseppe Rodriguez. 2023-11-27. Anti-Gauss cubature rules with applications to Fredholm integral equations on the square. https://doi.org/10.1137/24m1631432

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