An algorithm for the approximate solution of operator difference equations

Abstract

In this paper we consider a second order difference equation with variable coefficients in the field of Mikusiński operators, F, and construct an algorithm for its approximate solution. Also, we estimate the error of approximation and show that the approximate solution of this difference equation can be treated as the approximate solution of the corresponding differential equation in the field of Mikusiński, whose difference analogue turns out to be the considered difference equation.