Convergence of a simple discretization of the finite Hilbert transformation

03/23/2023

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by   {Martin Costabel, et al.

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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.