带端点一阶导数和三阶导数的中矩形修正公式  

A MODIFIED MID-RECTANGLE FORMULA WITH FIRST DERIVATIVE AND THIRD DERIVATIVE OF ENDPOINT

作　　者：杜跃鹏[1] 袁东锋[1] DU Yue-peng;YUAN Dong-feng(Nanyang Institute of Technology,Nanyang 473004,Chin)

机构地区：[1]南阳理工学院,河南南阳473004

出　　处：《南阳理工学院学报》2018年第2期106-109,共4页Journal of Nanyang Institute of Technology

摘　　要：利用代数精度的概念,构造出一种带端点一阶导数和三阶导数的中矩形修正公式,给出了公式的截断误差估计,并分析了复化公式的收敛阶。该修正公式具有5次代数精度,其复化公式比复化中矩形公式多计算两个端点的一阶导数和三阶导数各一次,收敛阶却比复化中矩形公式提高了4阶。数值算例验证了理论分析的正确性。Based on the concept of algebraic precision,a modified mid-rectangle formula with first derivative and third derivative of endpoint is constructed. The truncation error estimation of the formula is given and the convergence order of the complex formula is analyzed. The modified formula has five orders algebraic accuracy,the complex formula of which calculates respectively the first derivative and the third derivative of two endpoints more than once compared with the complex middle rectangular formula,and the convergence order is increased with additional four orders. Numerical examples verify the correctness of the theoretical analysis.

关 键 词：数值积分 中矩形公式 代数精度 截断误差 收敛阶 

分 类 号：O241.4[理学—计算数学]