On the solution of integral equations with strongly singular kernels

Kaya, A. C.; Erdogan, F.

doi:10.1090/qam/885173

Authors: A. C. Kaya and F. Erdogan
Journal: Quart. Appl. Math. 45 (1987), 105-122
MSC: Primary 45E99; Secondary 45L10, 65R20
DOI: https://doi.org/10.1090/qam/885173
MathSciNet review: 885173
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Abstract: In this paper some useful formulas are developed to evaluate integrals having a singularity of the form ${\left ( {t - x} \right )^{ - m}},m \ge 1$. Interpreting the integrals with strong singularities in the Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term ${\left ( {t - x} \right )^{ - m}}$, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

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