On numerical improvement of Gauss–Lobatto quadrature rules
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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.
论文关键词:Numerical integration,Gauss–Lobatto quadrature rule,Precision degree,The method of solving nonlinear systems,The method of undetermined coefficients
论文评审过程:Available online 24 November 2004.
论文官网地址:https://doi.org/10.1016/j.amc.2004.04.113