On the Eigenvalue Problem for the Discrete Analogue of the Laplace Operator in Spherical Coordinatesстатья
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Аннотация:The eigenvalue problem for the finite-differenced analogues of the Laplace operator inspherical coordinates is considered. Finding eigenvalues and eigenfunctions for the finite-differencedboundary settings is a useful tool when evaluating the conditions for the implementation of the socalledmatrix 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 onthe boundary values of potentials is given.