This article is cited in 1 paper

Partial Differential Equations

Explicit numerically implementable formulas for Poincaré–Steklov operators

A. S. Demidov^a, A. S. Samokhin<sup>b

a</sup> Lomonosov Moscow State University, 119991, Moscow, Russia
^b Institute of Control Sciences, Russian Academy of Sciences, 117997, Moscow, Russia

Abstract: 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.

Key words: Poincaré–Steklov operators, univalent isometric mapping of an analytic curve, explicit numerically implementable formulas.

UDC: 519.63

Received: 17.04.2023
Revised: 09.09.2023
Accepted: 20.10.2023

DOI: 10.31857/S0044466924020064

 English version: Computational Mathematics and Mathematical Physics, 2024, 64:2, 237–247

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