数值积分的校正公式研究

Research on correction formulas for numerical integration

讨论了积分校正公式的一般形式,利用代数精度的概念给出了确定了校正公式中的参数方法。给出了左矩形公式、梯形公式、辛甫生公式、一点高斯公式、二点高斯公式的校正公式,其它公式可类似处理。通过数值实例进行了比较。

The general forms of correction formulas for numerical integral are discussed.The parameters are obtained by theory of algebra accuracy.The correction formulas of left rectangle formula,trapezoid rule,Simpson＇s rule,one-point Gaussian quadrature rule and two-point Gaussian quadrature rule are given.The method in this paper can apply to various types of numerical integral formulas.At the same time,the methods are compared by a numerical example.