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：对于实轴区间上的奇异积分方程，我们研究了一种δ-δ离散化方法的误差行为。结果表明，收敛性是非均匀的：在区间内部误差阶为$O(h^{2})$，而在边界层处一致性误差趋近于非零值。