On numerical improvement of Gauss-Radau quadrature rules

It is known that Gauss-Radau quadrature rule∫-11f(x)dx≃∑i=1naif(bi)+pf(-1)(orqf(1)),is exact for polynomials of degree at most 2n. In this paper we intend to find a formula which is nearly exact for monomial functions xj, j = 0, 1, …, 2n + 2, instead of being analytically exact for the basis space xj, j = 0, 1, …, 2n. In this way, several examples are also given to show the numerical superiority of the presented rules with respect to usual Gauss-Radau quadrature rules.