摘要
用三角变量替换的方法把含Cauchy核的主值积分变换到[0,π)上含三角函数核的主值积分,用非等距结点的π(反)周期三角插值多项式作为工具去逼近新的主值积分的被积函数,构造出含Cauchy核主值积分的一个新的内插型求积公式,根据求积公式视结点个数的奇偶性不同给出了求积公式的不同表达式,推导出求积公式中求积系数的循环关系式.最后以一个实例在计算机上用Matlab编程实现,用得到的数值结果和图像来说明所得求积公式的误差渐进性.
Using the method of changing trigonometric variable, a principal value integral with Cauchy kernel was transformed to a principal value integral with trigonometric functions kernel. The new interpolatory-type quadrature quadrature formulae were constructed for the principal value integral with Cauchy kernel, in which the inteture forns of the coefficients were derived. Finally, the asymptotic error of the quadrature formulae was illustrated,using the numerical result and images from a case realized by Matlab.
出处
《武汉工程大学学报》
CAS
2015年第6期63-66,共4页
Journal of Wuhan Institute of Technology
基金
湖北省教育厅科研基金重点项目(D20101506)
关键词
Cauchy主值积分
三角插值
求积公式
Cauchy principal value integrals
trigonometric interpolation
quadrature formulae
