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Numerical methods for Fredholm integral equations with singular right-hand sides

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Abstract

Fredholm integral equations with the right-hand side having singularities at the endpoints are considered. The singularities are moved into the kernel that is subsequently regularized by a suitable one-to-one map. The Nyström method is applied to the regularized equation. The convergence, stability and well conditioning of the method is proved in spaces of weighted continuous functions. The special case of the weakly singular and symmetric kernel is also investigated. Several numerical tests are included.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Basilicata, v.le dell’Ateneo Lucano 10, 85100, Potenza, Italy

    L. Fermo & M. G. Russo

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  1. L. Fermo
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  2. M. G. Russo
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Correspondence to M. G. Russo.

Additional information

Communicated by Yuesheng Xu.

Dedicated to Prof. Giuseppe Mastroianni on the occasion of his 70th birthday.

Work supported by the research project PRIN 2006 of the Italian Ministry for the University and Research.

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Fermo, L., Russo, M.G. Numerical methods for Fredholm integral equations with singular right-hand sides. Adv Comput Math 33, 305–330 (2010). https://doi.org/10.1007/s10444-009-9137-4

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