, Volume 19, Issue 3, pp 248-259

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 uP(r 2)u=0; see [9].

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