On the solution of integral equations with strongly singular kernels

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 . 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 , 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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DOI:
https://doi.org/10.1090/qam/885173

Article copyright:
© Copyright 1987
American Mathematical Society