On numerical improvement of Gauss–Lobatto quadrature rules

摘要

It is well known that Gauss–Lobatto quadrature rule∫-11f(x)dx≃∑i=1nwif(xi)+pf(-1)+qf(1),is exact for polynomials of degree at most 2n + 1. In this paper we are going to find a formula which is approximately exact for monomials xj, j = 0, 1, …, 2n + 3 instead of being analytically exact for monomials xj, j = 0, 1, …, 2n + 1. We also consider a class of functions for which the new formula produces better results.