Newton-Cotes公式的渐近展开及其应用  

Asymptotic Expansion of Newton-Cotes Formula and Its Applications

作　　者：檀结庆[1] TAN Jieqing(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《大学数学》2024年第5期35-42,共8页College Mathematics

基　　金：国家自然科学基金(62172135)。

摘　　要：给出了(n+1)-点Newton-Cotes公式的渐近展开,作为特例,得到了梯形求积公式和Simpson求积公式及其复化形式的渐近展开,分析了与Euler-Maclaurin展开的区别与联系,指出从复化Simpson求积公式出发,可得到数值积分的高阶Romberg算法.The(n+1)-point Newton-Cotes formula for numerical integration is reformulated by expanding its remainder term into series,in particular,the expansions for trapezoidal rule,Simpson’s rule and their composite forms are obtained,and it is pointed out that the Romberg integration of higher order can also be worked out by applying the Richardson’s extrapolation to the presented expansion based on the composite Simpson’s rule instead of Euler-Maclaurin expansion.

关 键 词：Newton-Cotes公式 梯形求积公式 渐近展开 Euler-Maclaurin展开 

分 类 号：O241[理学—计算数学]