| 圆周上带希尔伯特核的柯西奇异积分方程的数值解(英文) |
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| 引用本文： | 刘扬,宋兵.圆周上带希尔伯特核的柯西奇异积分方程的数值解(英文)[J].数学杂志,2012,32(4):582-588. |
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| 作者姓名： | 刘扬 宋兵 |
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| 作者单位： | 1. 武汉大学数学与统计学院,湖北武汉430072;武汉理工大学理学院,湖北武汉430070
2. 武汉外国语学校,湖北武汉,430022 |
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| 基金项目： | Supported by National Natural Science Foundation of China(10671182);the Fundamental Research Funds for the Central Universities(2011-la-012) |
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| 摘 要： | 本文研究了圆周上带希尔伯特核的柯西奇异积分的复合梯型公式.利用连续的分片线性函数逼近被积函数,得到积分公式的误差估计;然后用积分公式构造求解对应奇异积分方程的两种格式;最后给出数值实验验证理论分析结果.
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| 关 键 词： | Hilbert变换 奇异积分方程 Cauchy主值积分 配置法 |
NUMERICAL SOLUTION OF CAUCHY SINGULAR INTEGRAL EQUATIONS WITH HILBERT KERNEL ON THE CIRCLE |
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| LIU Yang
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SONG Bing.NUMERICAL SOLUTION OF CAUCHY SINGULAR INTEGRAL EQUATIONS WITH HILBERT KERNEL ON THE CIRCLE[J].Journal of Mathematics,2012,32(4):582-588. |
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| Authors: | LIU Yang SONG Bing |
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| Institution: | 1.School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)(2.School of Science,Wuhan University of Technology,Wuhan 430070,China)(3.Wuhan Foreign Languages School,Wuhan 430022,China) |
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| Abstract: | In this paper,we first investigate the composite trapezoidal rule for the evaluation of Cauchy principle value integral with Hilbert kernel on a circle.By using continuous piecewise linear function to approximate density function,we get the error estimation of numerical integral.Then we apply the rule to construct two schemes for solving the relevant singular integral equation.Some numerical experiments are presented to confirm the theoretical analysis at last. |
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| Keywords: | Hilbert transform singular integral equation Cauchy principal value integral collocation method |
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