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<p>This paper uses the finite difference method for elliptic problems with nonlocal boundary conditions. We study the case where the matrix of the resulting system of linear equations is an <i>M</i>-matrix. We present the main properties of monotone matrices and <i>M</i>-matrices. The finite difference method is considered for the two-dimensional Poisson equation with Dirichlet boundary condition, and for the same one-dimensional problem with two integral conditions. Sufficient conditions for the problem to be described by an <i>M</i>-matrix or a monotone matrix is formulated using the parameters of nonlocal boundary conditions. Other types of nonlocal boundary conditions are investigated in the one-dimensional case.</p>

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M-matrices and discrete problems with nonlocal boundary conditions

  • 期刊论文

  • 发表日期：

    2025年4月17日

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  • Vytautas Būda,
  • Mifodijus Sapagovas,
  • Olga Štikonienė,
  • Artūras Štikonas

摘要

This paper uses the finite difference method for elliptic problems with nonlocal boundary conditions. We study the case where the matrix of the resulting system of linear equations is an M-matrix. We present the main properties of monotone matrices and M-matrices. The finite difference method is considered for the two-dimensional Poisson equation with Dirichlet boundary condition, and for the same one-dimensional problem with two integral conditions. Sufficient conditions for the problem to be described by an M-matrix or a monotone matrix is formulated using the parameters of nonlocal boundary conditions. Other types of nonlocal boundary conditions are investigated in the one-dimensional case.