带端点3阶导数的Simpson修正公式

journal6 ›› 2008, Vol. 29 ›› Issue (4): 20-23.

带端点3阶导数的Simpson修正公式

（南阳理工学院，河南南阳 473000）

出版日期:2008-07-25 发布日期:2012-05-21
作者简介:肖泽昌（1963-），男，河南南阳人，南阳理工学院副教授，主要从事计算数学研究；杜跃鹏（1965-），男，河南南阳人，南阳理工学院计算机科学与技术系副教授，硕士，主要从事计算数学研究.

Modified Formula for Simpson Rule with Third Derivatives of Endpoint

（Nanyang Institute of Technology,Nanyan 473000,Henan China）

Online:2008-07-25 Published:2012-05-21

摘要/Abstract

摘要：给出了一个带端点3阶导数的Simpson修正公式，并给出该公式的截断误差，分析了相应的复化公式的收敛阶.复化带端点3阶导数的Simpson修正公式，只比复化Simpson公式多计算2个端点的3阶导数各1次，其收敛阶却比复化Simpson公式提高了2阶.数值算例验证了理论分析的正确性.

关键词： 数值积分, Simpson公式, 代数精度, 截断误差, 收敛阶

Abstract: This paper presents a modified formula for Simpson rule with third derivatives of endpoint and its truncation error.It also displays an analysis on convergence order of compound formula.Though compound modified formula for Simpson rule with endpoint derivatives just calculates a newly-added third derivative of the two endpoints for each time compared with compound Simpson formula calculation,there are 2 more ranks of the convergence order in this modified formula.Examples of numerical calculation have validated theoretical analysis.

Key words: numerical integration, Simpson formula, algebraic accuracy, truncation error, convergence order

肖泽昌, 杜跃鹏. 带端点3阶导数的Simpson修正公式[J]. journal6, 2008, 29(4): 20-23.

XIAO Ze-Chang, DU Yue-Peng. Modified Formula for Simpson Rule with Third Derivatives of Endpoint[J]. journal6, 2008, 29(4): 20-23.