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The numerical solution of Fredholm integral equations of the second kind with singular kernels

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Abstract

A numerical method is given for integral equations with singular kernels. The method modifies the ideas of product integration contained in [3], and it is analyzed using the general schema of [1]. The emphasis is on equations which were not amenable to the method in [3]; in addition, the method tries to keep computer running time to a minimum, while maintaining an adequate order of convergence. The method is illustrated extensively with an integral equation reformulation of boundary value problems forΔ u−P(r 2)u=0; see [9].

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Author notes

  1. Kendall Atkinson

    Present address: Research Fellow at Computer Center, Australian National University, Canberra, Australia

Authors and Affiliations

  1. Mathematics Department, Indiana University, 47401, Bloomington, Indiana, USA

    Kendall Atkinson

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  1. Kendall Atkinson
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This research was supported in part by NSF grant GP-8554.

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Atkinson, K. The numerical solution of Fredholm integral equations of the second kind with singular kernels. Numer. Math. 19, 248–259 (1972). https://doi.org/10.1007/BF01404695

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