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

作者：Yuezbasi Suayip

来源：Computers & Mathematics with Applications, 2011, 62(5): 2289-2303.

DOI：10.1016/j.camwa.2011.07.016

• Singular differential-difference equations
• Approximate solutions
• Collocation method
• Collocation points
• The Bessel matrix method
• The Bessel polynomials and series

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).

• 出版日期2011-9