Numerical approach of linear delay difference equations with variable coefficients in terms of Bernoulli polynomials

The aim of this study is to give a Bernoulli polynomial approximation for the solution of linear delay difference equations with variable coefficients under the mixed conditions about any point. For this purpose, Bernoulli matrix method is introduced. This method transforms linear delay difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. In addition, examples that illustrate the pertinent features of the method are presented, and the results of study are discussed. Also we have discussed the accuracy of the method.