带端点5阶导数的Cotes修正公式

数学季刊 ›› 2009, Vol. 24 ›› Issue (4): 585-589.

带端点5阶导数的Cotes修正公式

1. Department of Basic Course, Henan Quality and Engineering Vocational College2. Professional College of Information and Statistics, Zhengzhou Institute of Aeronautical Industry Management

收稿日期:2006-06-06 出版日期:2009-12-30 发布日期:2023-06-19
作者简介: SUN Fan(1972-), female, native of Pingdingshan, Henan, a lecturer of Henan Quality and Engineering Vocational College, M.S.D., engages in higher mathematics education teaching and research.
基金资助:

Modified Formula for Cotes Rule with Fifths Derivatives of Endpoint

1. Department of Basic Course, Henan Quality and Engineering Vocational College2. Professional College of Information and Statistics, Zhengzhou Institute of Aeronautical Industry Management

Received:2006-06-06 Online:2009-12-30 Published:2023-06-19
About author: SUN Fan(1972-), female, native of Pingdingshan, Henan, a lecturer of Henan Quality and Engineering Vocational College, M.S.D., engages in higher mathematics education teaching and research.

摘要/Abstract

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

关键词: numerical integration, algebraic precision, truncation error, order of convergence

Abstract: This paper presents a Modified Formula for Cotes rule with fifths derivatives of endpoint and its truncation error. It also displays an analysis on convergence order of compound formula. Though compound modified formula for Cotes rule with endpoint derivatives just calculates a newly-added fifths derivative of the two endpoints for each time compared with compound Cotes 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, algebraic precision, truncation error, order of convergence

中图分类号:

O241.4

孙帆, 韩可众. 带端点5阶导数的Cotes修正公式[J]. 数学季刊, 2009, 24(4): 585-589.

SUN Fan, HAN Ke-zhong. Modified Formula for Cotes Rule with Fifths Derivatives of Endpoint [J]. Chinese Quarterly Journal of Mathematics, 2009, 24(4): 585-589.

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