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

Abstract

A strongly singular linear integral equation containing a small positive parameter δ \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 ( δ 2 ) o\left ( {{\delta ^2}} \right ) . An example from fracture mechanics is considered in detail.