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Abstract <p>The eigenvalue problem for the finite-differenced analogues of the Laplace operator in spherical coordinates is considered. Finding eigenvalues and eigenfunctions for the finite-differenced boundary settings is a useful tool when evaluating the conditions for the implementation of the so-called matrix sweep method. This method makes it possible to determine potentials in two cases: (a)&#xa0;when the discrete fundamental solution is known, and (b) if an additional a priori information on the boundary values of potentials is given.</p>

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On the Eigenvalue Problem for the Discrete Analogue of the Laplace Operator in Spherical Coordinates

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • I. E. Stepanova,
  • A. V. Shchepetilov,
  • I. I. Kolotov

摘要

Abstract

The eigenvalue problem for the finite-differenced analogues of the Laplace operator in spherical coordinates is considered. Finding eigenvalues and eigenfunctions for the finite-differenced boundary settings is a useful tool when evaluating the conditions for the implementation of the so-called matrix sweep method. This method makes it possible to determine potentials in two cases: (a) when the discrete fundamental solution is known, and (b) if an additional a priori information on the boundary values of potentials is given.