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Mathematical notes of NEFU, 2025, Volume 32, Issue 4, Pages 67–81 (Mi svfu494)

Mathematics

Screened harmonic system with Dirichlet and Neumann boundary conditions in analysis in the three-dimensional case

M. P. Eremchuk, A. L. Ushakov

South Ural State University, Chelyabinsk

Abstract: A screened harmonic system with Dirichlet and Neumann boundary conditions is analyzed in the three-dimensional case. This system is continued through boundaries with Dirichlet and Neumann conditions. The system of linear algebraic equations obtained after discretization of the continued system is considered. An asymptotically optimal analysis is given for the discrete continued system. The method for analyzing the discrete continued system is implemented in the algorithm.

Keywords: asymptotically optimal analysis, screened harmonic system, Dirichlet boundary condition, Neumann boundary condition

UDC: 519.63

Received: 12.05.2025
Accepted: 01.12.2025

DOI: 10.25587/2411-9326-2025-4-66-80



© Steklov Math. Inst. of RAS, 2026