On the discrete Dirichlet problem in a quarter plane

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.