Abstract
We study a discrete analogue on the Neumann boundary value problem for elliptic pseudo-differential equation in a quadrant. This approach is based on a special factorization of an elliptic symbol which permits to construct a general solution for a discrete pseudo-differential equation in discrete analogues of Sobolev–Slobodetskii spaces. The discrete Neumann boundary conditions are considered in the paper. Unique solvability of discrete Neumann boundary value problem is proved and a comparison between discrete and continuous solutions is given.
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Mashinets, A.A., Vasilyev, A.V. & Vasilyev, V.B. On Discrete Neumann Problem in a Quadrant. Lobachevskii J Math 44, 1018–1028 (2023). https://doi.org/10.1134/S1995080223030216
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DOI: https://doi.org/10.1134/S1995080223030216