[1]马达,章文勋,张善杰.负参数Mathieu 函数类的计算[J].东南大学学报(自然科学版),2010,40(1):11-17.[doi:10.3969/j.issn.1001-0505.2010.01.003]
 Ma Da,Zhang Wenxun,Zhang Shanjie.Calculations of Mathieu functions with negative parameter[J].Journal of Southeast University (Natural Science Edition),2010,40(1):11-17.[doi:10.3969/j.issn.1001-0505.2010.01.003]
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负参数Mathieu 函数类的计算()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
40
期数:
2010年第1期
页码:
11-17
栏目:
信息与通信工程
出版日期:
2010-01-20

文章信息/Info

Title:
Calculations of Mathieu functions with negative parameter
作者:
马达1 章文勋1 张善杰2
1 东南大学毫米波国家重点实验室,南京 210096; 2 南京大学电子科学与工程系,南京 210093
Author(s):
Ma Da1 Zhang Wenxun1 Zhang Shanjie2
1 State Key Laboratory of Millimeter Waves,Southeast University,Nanjing 210096,China
2 Department of Electronic Science and Engineering,Nanjing University,Nanjing 210093,China
关键词:
负参数Mathieu函数 负参数Mathieu导函数 程序包
Keywords:
Mathieu functions with negative parameter derivative of Mathieu functions with negative parameter routine package
分类号:
TN911.1
DOI:
10.3969/j.issn.1001-0505.2010.01.003
摘要:
为解决实际工程尤其是电磁场问题中需要计算负参数Mathieu函数精确值的难题,在总结了含正、负参数的Mathieu函数之间变换关系的基础上,推导出了各类含负参数Mathieu导函数的叠加计算公式.并据此编制了各类含负参数Mathieu函数及其导函数的计算程序,给出相应的计算数表和函数曲线.通过与商业软件、参考文献及标准数学手册的对比,验证了计算结果的准确性和可靠性,修正并补充了参考文献和数学手册中的部分结果.所编制的Matlab程序包为实际工程应用中计算Mathieu函数类提供了有效的计算工具.
Abstract:
In order to calculate the accurate values of Mathieu functions with negative parameters in actual engineering, especially in electromagnetic field problems, the derivatives of Mathieu functions with negative parameter are deduced firstly based on the transformation between the Mathieu functions with positive and negative parameters. The subroutines for calculation of Mathieu functions are programmed. Some calculated results are represented in tables and curves, which are reliable in comparison with those by using other software, references and standard handbook of mathematics. Therefore, the subroutine package with Matlab language is an effective tool for calculation of Mathieu functions with negative parameters in practical application.

参考文献/References:

[1] 章文勋. 无线电技术中的微分方程[M].北京:国防工业出版社,1982:82-92.
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  Sui Guofang,Ding Zhilai.A numerical method of Mathieu functions[J].Journal of Numerical Methods and Computer Applications,1987(3):165-170.(in Chinese)
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[8] Zhang S J,Shen Y C.Eigenmode sequence for an elliptical waveguide with arbitrary ellipticity [J].IEEE Trans Microwave Theory and Tech,1995,43(1):227-230.
[9] Zhang S J,Jin J M.Computation of special functions [M].New York:John Wiley & Sons,1996:475-535.
[10] 张善杰,沈耀春.马丢函数的数值计算[J].电子学报,1995,23(9):41-46.
  Zhang Shanjie,Shen Yaochun.Numerical computation of Mathieu functions[J].Acta Electronica Sinica,1995,23(9):41-46.(in Chinese)

备注/Memo

备注/Memo:
作者简介: 马达(1983—),男,博士生; 章文勋(联系人),男,教授,博士生导师,wxzhang37@yahoo.com.cn.
基金项目: 国家自然科学创新群体基金资助项目(60621002)、江苏省普通高校研究生科研创新计划资助项目.
引文格式: 马达,章文勋,张善杰.负参数Mathieu 函数类的计算[J].东南大学学报:自然科学版,2010,40(1):11-17. [doi:10.3969/j.issn.1001-0505.2010.01.003]
更新日期/Last Update: 2010-01-20