| 二重积分integral from n=a to b(dx) integral from n=c to d (f(x,y)dy)的柯特斯公式及其误差分析 |
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| 引用本文： | 兰亭,邹佳利,覃燕梅.二重积分integral from n=a to b(dx) integral from n=c to d (f(x,y)dy)的柯特斯公式及其误差分析[J].保山学院学报,2012(2):60-63. |
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| 作者姓名： | 兰亭 邹佳利 覃燕梅 |
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| 作者单位： | 内江师范学院四川省高等学校数值仿真实验室/数学与信息科学学院 |
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| 摘 要： | 重积分是高等数学的主要内容之一。柯特斯公式是定积分数值算法的一种重要方法,其具有误差精度高的优点,误差精度可达到6阶,将结合定积分柯特斯公式与二重积分的特点,将柯特斯公式推广到二重积分的情形。首先,给出了柯特斯公式的表达式及其误差公式;然后,将定积分的柯特斯公式推广到二重积分的情形,并结合积分中值定理推出其误差表达式。误差结果表明,推广到二重积分后的柯特斯公式仍具有6阶精度。
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| 关 键 词： | 二重积分 柯特斯公式 误差分析 |
The Cotes formula of Double Integration integral from n=a to b(dx) integral from n=c to d (f(x,y)dy) and error analysis |
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| Lan Ting Zou Jia-li Qin Yan-mei.The Cotes formula of Double Integration integral from n=a to b(dx) integral from n=c to d (f(x,y)dy) and error analysis[J].Journal of Baoshan Teachers College,2012(2):60-63. |
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| Authors: | Lan Ting Zou Jia-li Qin Yan-mei |
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| Institution: | Lan Ting Zou Jia-li Qin Yan-mei(Key Laboratory of Numerical Simulation in the Sichuan Provincial College/College of Mathematics and Information Sciences of Neijiang Normal University Neijiang,Sichuan Province 641000,China) |
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| Abstract: | Re-integration is one of the main elements of higher mathematics.Cotes integration formula is an important method of numerical algorithm,which has sixth-order precision.In this paper,the Cotes formula will be extended to the double integral case.Firstly,the Cotes formula and its error formula are given.Secondly,the new Cotes formula of double integral is given,and the error is expressed by value theorem of integral.The error results showed that the new Cotes formula of double integral still has the sixth-order precision. |
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| Keywords: | double integral Cotes formula error analysis |
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