| 带端点3阶导数的Simpson修正公式 |
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| 引用本文： | 肖泽昌,杜跃鹏.带端点3阶导数的Simpson修正公式[J].吉首大学学报(自然科学版),2008,29(4):20-23. |
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| 作者姓名： | 肖泽昌 杜跃鹏 |
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| 作者单位： | （南阳理工学院，河南 南阳 473000） |
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| 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.
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| 关 键 词： | 数值积分 Simpson公式 代数精度 截断误差 收敛阶 |
Modified Formula for Simpson Rule with Third Derivatives of Endpoint |
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| XIAO Ze-chang,DU Yue-peng.Modified Formula for Simpson Rule with Third Derivatives of Endpoint[J].Journal of Jishou University(Natural Science Edition),2008,29(4):20-23. |
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| Authors: | XIAO Ze-chang DU Yue-peng |
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| Institution: | （Nanyang Institute of Technology,Nanyan 473000,Henan China） |
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| 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. |
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| Keywords: | numerical integration Simpson formula algebraic accuracy truncation error convergence order |
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