For a singular integral equation on an interval of the real line, we study the behavior of the error of a delta-delta discretization. We show that the convergence is non-uniform, between order $O(h^{2})$ in the interior of the interval and a boundary layer where the consistency error does not tend to zero.

翻译：针对实直线区间上的奇异积分方程，我们研究了δ-δ离散化误差的行为特征。结果表明，收敛性是非均匀的：在区间内部可达$O(h^{2})$阶收敛，而在边界层区域一致性误差不趋于零。