Geodesic
On discrete boundary-value problems in a~quarter plane
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 14-23

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We consider a discrete elliptic pseudodifferential equation in a quadrant and the corresponding discrete boundary-value problem. Conditions for the solvability of the discrete boundary-value problem in discrete analogs of the Sobolev–Slobodetskii spaces are described. The discrete solution is compared with the solution of the corresponding continuum boundary-value problem depending on the discretization parameter.
Keywords: discrete pseudodifferential operator, two-dimensional periodic Riemann problem, periodic wave factorization, analyticity, solvability. 
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     title = {On discrete boundary-value problems in a~quarter plane},
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V. B. Vasilev (Vasilyev); A. A. Khodyreva. On discrete boundary-value problems in a~quarter plane. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 14-23. http://geodesic.mathdoc.fr/item/INTO_2023_223_a1/