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Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions

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Abstract

In a rectangular domain, we consider the two-dimensional Poisson equation with nonlocal boundary conditions in one of the directions. For this problem, we construct a difference scheme of fourth-order approximation, study its solvability, and justify an iteration method for solving the corresponding system of difference equations. We give a detailed study of the spectrum of the matrix representing this system. In particular, we obtain a criterion for the nondegeneracy of this matrix and conditions for its eigenvalues to be positive.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Vilnius, Lithuania

    M. P. Sapagovas

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  1. M. P. Sapagovas
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Original Russian Text © M.P. Sapagovas, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 7, pp. 988–998.

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Sapagovas, M.P. Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions. Diff Equat 44, 1018–1028 (2008). https://doi.org/10.1134/S0012266108070148

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  • DOI: https://doi.org/10.1134/S0012266108070148

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