On the solution to a class of strongly singular linear integral equations

Gautesen, A. K.

doi:10.1090/qam/1146628

Author: A. K. Gautesen
Journal: Quart. Appl. Math. 50 (1992), 129-140
MSC: Primary 45G05
DOI: https://doi.org/10.1090/qam/1146628
MathSciNet review: MR1146628
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Abstract: A strongly singular linear integral equation containing a small positive parameter $\delta$ is considered. This equation is transformed into a Fredholm integral equation of the second kind with a continuous kernel. The rate of convergence of the Neumann series for this integral equation is shown to be $o\left ( {{\delta ^2}} \right )$. An example from fracture mechanics is considered in detail.

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