Geodesic
On the discrete Dirichlet problem in a quarter plane
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 34-46

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In this paper, we consider a discrete elliptic pseudodifferential equation in a quadrant and the related discrete Dirichlet boundary-value problem and discuss conditions for the solvability of a discrete boundary-value problem in discrete analogs of the Sobolev–Slobodetsky spaces. We compare discrete solutions with solutions of the corresponding continual boundary-value problem depending on the discretization parameter.
Keywords: discrete pseudodifferential operator, periodic wave factorization, analyticity, solvability, discrete Dirichlet problem. 
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     author = {V. B. Vasilev (Vasilyev) and A. A. Khodyreva},
     title = {On the discrete {Dirichlet} problem in a quarter plane},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {34--46},
     publisher = {mathdoc},
     volume = {226},
     year = {2023},
     language = {ru},
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V. B. Vasilev (Vasilyev); A. A. Khodyreva. On the discrete Dirichlet problem in a quarter plane. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 34-46. http://geodesic.mathdoc.fr/item/INTO_2023_226_a3/