Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions |
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Authors: | M P Sapagovas |
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Institution: | 1.Institute of Mathematics and Informatics,Vilnius,Lithuania |
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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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