Convergence of a simple discretization of the finite Hilbert transformation

Abstract

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.

14 pages

References in corpus (2)

• The discrete dipole approximation: an overview and recent developments
• Convergence of the discrete dipole approximation. I. Theoretical analysis