Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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 $ {\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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DOI: https://doi.org/10.1090/qam/885173
Article copyright: © Copyright 1987 American Mathematical Society


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