Numerical Treatment of a Skew-Derivative Problem for the Laplace Equation in the Exterior of Open Arcs: One-Point Scheme

We consider a skew derivative problem for a function which is harmonic in the exterior of open arcs in a plane. This problem models electric current in a semiconductor film from electrodes of arbitrary shapes in the presence of a magnetic field. A numerical method for solving the problem is proposed. The method is based on the boundary integral equation approach. The proposed numerical method is tested for different values of parameters and different shapes of the electrodes.