Explicit Numerically Implementable Formulas for Poincaré–Steklov Operators

The paper presents explicit numerically implementable formulas for the Poincaré–Steklov operators, such as the Dirichlet–Neumann, Dirichlet–Robin, Robin1–Robin2, and Grinberg–Mayergoiz operators, related to the two-dimensional Laplace equation. These formulas are based on the lemma about a univalent isometric mapping of a closed analytic curve onto a circle. Numerical results for domains with very complex geometries were obtained for several test harmonic functions for the Dirichlet–Neumann and Dirichlet–Robin operators.