Determination of nodes in numerical integration rules using difference equation

In this paper, the difference equations will be employed to produce a polynomial which its roots are the nodes of Gauss quadrature rules. In this procedure, we obtain a system of nonlinear equations according to the concepts of precision degree of integration and the moments of order k. Hence the resulted polynomials obtained by difference equations have their roots as the nodes. Finally, some examples are given to show the application of the procedure.