This paper is concerned with the numerical approximation of Fredholm integral equa- tions of the second kind. A Nyström method based on the anti-Gauss quadrature formula is developed and investigated in terms of stability and convergence in appro- priate weighted spaces. The Nyström interpolants corresponding to the Gauss and the anti-Gauss quadrature rules are proved to furnish upper and lower bounds for the solution of the equation, under suitable assumptions which are easily verified for a particular weight function. Hence, an error estimate is available, and the accuracy of the solution can be improved by approximating it by an averaged Nyström interpolant. The effectiveness of the proposed approach is illustrated through different numerical tests.

Solution of second kind Fredholm integral equations by means of Gauss and anti-Gauss quadrature rules

Fermo ;Luisa;Rodriguez; Giuseppe
2020

Abstract

This paper is concerned with the numerical approximation of Fredholm integral equa- tions of the second kind. A Nyström method based on the anti-Gauss quadrature formula is developed and investigated in terms of stability and convergence in appro- priate weighted spaces. The Nyström interpolants corresponding to the Gauss and the anti-Gauss quadrature rules are proved to furnish upper and lower bounds for the solution of the equation, under suitable assumptions which are easily verified for a particular weight function. Hence, an error estimate is available, and the accuracy of the solution can be improved by approximating it by an averaged Nyström interpolant. The effectiveness of the proposed approach is illustrated through different numerical tests.
second kind integral equation; Nystrom method; anti-Gauss quadrature
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/301819
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