| 基于积分的数值微分算法 |
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| 引用本文： | 徐会林,郜星军.基于积分的数值微分算法[J].江西科学,2014(1):1-4,7. |
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| 作者姓名： | 徐会林 郜星军 |
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| 作者单位： | 河南理工大学数学与信息科学学院,河南焦作454000 |
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| 基金项目： | 国家自然科学基金（11226319）;河南省教育厅科学技术研究重点项目（13A110345）;国家级大学生创新项目（201310460007）. |
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| 摘 要： | 利用微分与积分之间的互逆关系,给出了基于积分的数值微分算法,其实质是将数值微分问题等价转化为第一类积分方程的求解问题。借助数值积分法求解第一类的积分方程,给出了一元函数前两阶导数的近似计算方法,并通过算例说明了该方法的数值有效性。
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| 关 键 词： | 数值微分 积分 积分方程 数值算法 |
A Numerical Differentiation Method Based on the Integration |
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| XU Hui-lin,GAO Xing-jun.A Numerical Differentiation Method Based on the Integration[J].Jiangxi Science,2014(1):1-4,7. |
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| Authors: | XU Hui-lin GAO Xing-jun |
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| Institution: | ( School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454000 PRC) |
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| Abstract: | Considering the inverse relation between the differentiation and integration, we give a nu-merical differentiation method based on the integration. Its essence is to rewrite the numerical differ-entiation problem as an integral equation of the first kind. With the help of the numerical integration method for solving the integral equation of the first kind, we give some approximate computing meth-ods for the first two order numerical derivatives, and show its numerical validity by examples. |
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| Keywords: | Numerical differentiation Integration Integral equation Numerical algorithm |
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