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- Title
Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions.
- Authors
Sapagovas, M.
- 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.
- Subjects
GEOMETRY; MATRICES (Mathematics); EIGENVALUES; MATRIX inequalities; HOUGH functions; FATOU theorems; ASYMPTOTIC expansions; POISSON'S equation
- Publication
Differential Equations, 2008, Vol 44, Issue 7, p1018
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266108070148