On explicit numerically realizable formulae for Poincaré-Steklov operators

DOI10.4213/RM10118EMaRDI QIDQ6492367

Aleksander S. Demidov

Publication date: 25 April 2024

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solutions to equations with nonlinear operators (65J15) Representations of solutions to partial differential equations (35C99)

Cites Work

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• Numerical solution of the Robin problem of Laplace equations with a Feynman-Kac formula and reflecting Brownian motions
• On numerically implementable explicit formulas for the solutions to the 2D and 3D equations \(\operatorname{div}(\alpha(w)\nabla w)=0\) and \(\operatorname{div}(\beta\nabla w)=0\) with Cauchy data on an analytic boundary
• On the numerical solution of boundary value problems in potential theory by the method of integral equations
• The method of potentials and the numerical solution of Dirichlet' s problem for the Laplace equation

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