Construction of the solutions of difference equations in the field of mikusiński operators

Abstract

We construct the solutions of certain difference equations with variable coefficients in the field of Mikusiński operators F. The method we are using is very similar to the method used for the difference equations with variable numerical coefficients. We analyze the character of the solutions of the difference equation obtained by using this method. The considered difference equations can be treated as the discrete analogues for the differential equations whose coefficients are operator functions in the field F. Therefore the obtained solutions can be treated as the approximate solutions for the corresponding differential equations. © 1997 Rocky Mountain Mathematics Consortium © 1997 Applied Probability Trust.