Numerical estimation of the coefficient of the homogenous Riemann-Hilbert problem on the basis of boundary data

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The coefficient of the classical homogeneous Riemann-Hilbert boundary value problem in complex analysis is evaluated by using an appropriate complex integral on a closed contour surrounding the arc where the problem is defined. Numerical interaction rules for complex contour integrals are used. Only the numerical values of the sectionally analytic function which is the solution of the problem are required (at the nodes of the quadrature rule). Numerical results in a few applications are displayed, and the rapid convergence of the approach is clearly observed. The present results are applicable to a large class of physical and engineering problems, e.g., to the interface crack problem in classical plane elasticity.