A numerical approach for solving the high-order linear singular differential-difference equations. (English) Zbl 1231.65252
Summary: 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).
MSC:
| 65Q10 | Numerical methods for difference equations |
| 34K07 | Theoretical approximation of solutions to functional-differential equations |
Keywords:
singular differential; difference equations; approximate solutions; collocation method; collocation points; the Bessel matrix method; MATLAB v7.6.0 (R2008a); Bessel polynomials and seriesSoftware:
MatlabReferences:
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