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Difference Approach to Solving Boundary Value Problems for Elliptic Partial Differential Equations in the Sense of Generalized Functions

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Abstract

An approach is described for constructing homogeneous difference schemes using difference analogs of partial derivatives of regular generalized functions. Homogeneous difference operator schemes on an irregular three simplicial grid corresponding to the Dirichlet and Robin boundary value problems for an elliptic differential equation are considered as examples.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    M. N. Sablin

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  1. M. N. Sablin
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Correspondence to M. N. Sablin.

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Translated by I. Obrezanova

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Sablin, M.N. Difference Approach to Solving Boundary Value Problems for Elliptic Partial Differential Equations in the Sense of Generalized Functions. MoscowUniv.Comput.Math.Cybern. 46, 29–41 (2022). https://doi.org/10.3103/S0278641922010058

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  • DOI: https://doi.org/10.3103/S0278641922010058

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