On Discrete Solutions for Elliptic Pseudo-Differential Equations

Abstract

We consider discrete analogue for simplest boundary value problem for elliptic pseudo-differential equation in a half-space with Dirichlet boundary condition in Sobolev-Slobodetskii spaces. Based on the theory of discrete boundary value problems for elliptic pseudo-differential equations we give a comparison between discrete and continuous solutions for certain model boundary value problem.

Keywords

• Digital pseudo-differential operator
• Discrete solution
• Discrete boundary value problem
• Rate of approximation