Correction Formulas For Gauss-Legendre Quadrature

Based on Gauss integration, this paper introduces in detail Gauss-Legendre quadratrue formulas, and two deformation formulas of the Gauss-Legendre quadratrue formulas: corrective Gauss-Legendre quadratrue formulas and numerical improvement of Gauss-Legendre quadratrue formulas. One of them comes from the integral remainder term and when the Integral interval endpoints is regard to be undetermined constants, we get the other. Through analyzing, this paper have attested that corrective Gauss-Legendre quadratrue formulas with two higher order algebraic precision than the corresponding Gauss-Legendre formulas. Therefore corrective Gauss-Legendre quadratrue formulas can effectively improve the accuracy of numerical integration. However , numerical improvement of Gauss-Legendre quadratrue formulas could improve slightly under more strictly conditions. And , with the help of MATLAB Software, this article designs a series of numerical experimentation schemes to compare Gauss-Legendre, JZGL and NIGL quadratrue formulas and their composite formulas with respect to accuracy.