Taylor collocation method for systems of high-order linear differential–difference equations with variable coefficients

A Taylor collocation method has been developed to solve the systems of high-order linear differential–difference equations in terms of the Taylor polynomials. Using the Taylor collocation points, this method transforms differential–difference equation systems and the given conditions to matrix equations with unknown Taylor coefficients. By means of the obtained matrix equation, a new system of equations corresponding to the system of linear algebraic equations is gained. Hence, by finding the Taylor coefficients easily, Taylor polynomial solutions are obtained. To illustrate the pertinent features examples are presented and results are compared. All numerical computations have been performed on the computer algebraic system Maple 9.