An approach to numerical solutions of system of high-order linear differential-difference equations with variable coefficients and error estimation based on residual function

In this study a method is presented which aims to make an approach by using Bernstein polynomials to solutions of systems of high order linear differential-difference equations with variable coefficients given under mixed conditions. The method converts a given system of differential-difference equations and the conditions belonging to this system to equations that can be expressed by matrices by using the collacation points and provides to find the unknown coefficients of approximate solutions sought in terms of Bernstein polynomials. Different examples are presented with the purpose to show the applicability and validity of the method. Absolute error values between exact and approximate solutions are computed. The estimated values of absolute errors are computed by using the residual function and these estimated errors are compared with absolute errors. For all numerical computations of this study the computer algebraic system Maple 15 is used.