| 基于非线性变量替换的数值积分方法 |
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| 引用本文： | 林福荣,陈琼生. 基于非线性变量替换的数值积分方法[J]. 汕头大学学报(自然科学版), 2010, 25(3): 20-25 |
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| 作者姓名： | 林福荣 陈琼生 |
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| 作者单位： | 汕头大学数学系,广东,汕头,515063 |
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| 摘 要： | 讨论两类积分的数值计算方法.一类是定义在很大的有限区间上的积分,其被积函数在一个端点附近变化比较快,而在另一个端点附近变化很慢;另一类是无穷区间上的积分.针对这两种类型积分的特点,分别构造适当的非线性变量替换,使得数值积分的精度大幅度提高.最后给出数值例子.
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| 关 键 词： | 数值积分 Clenshaw-Curtis求积方法 非线性变量替换 |
Numerical Quadratures Based on Nonlinear Variable Substitution |
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| LIN Fu-rong,CHEN Qiong-sheng. Numerical Quadratures Based on Nonlinear Variable Substitution[J]. Journal of Shantou University(Natural Science Edition), 2010, 25(3): 20-25 |
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| Authors: | LIN Fu-rong CHEN Qiong-sheng |
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| Affiliation: | (Department of Mathematics,Shantou University,Shantou 515063,Guangdong,China) |
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| Abstract: | This paper is concerned with numerical quadratures based on nonlinear variable substitution.Two types of integrals are considered.In the first type of integrals,it is assumed that the integration interval is very large,and the integrand varies quickly near one end while it varies very slowly near another end.In the second type of integrals,the integration interval is infinite.Suitable nonlinear variable substitutions are introduced for these integrals to obtain high accurate numerical quadratures.Numerical results are given to illustrate the accuracy of the proposed quadratures. |
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| Keywords: | numerical quadrature Clenshaw-Curtis quadrature nonlinear variable substitution |
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