A numerical approach for solving the high-order linear singular differential–difference equations

In this paper, a numerical method which produces an approximate polynomial solution is presented for solving the high-order linear singular differential–difference equations. With the aid of Bessel polynomials and collocation points, this method converts the singular differential–difference equations into the matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. This method gives the analytic solutions when the exact solutions are polynomials. Finally, some experiments and their numerical solutions are given; by comparing the numerical results obtained from the other methods, we show the high accuracy and efficiency of the proposed method. All of the numerical computations have been performed on a PC using some programs written in MATLAB v7.6.0 (R2008a).