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.
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 func- tions 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.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2010年第1期11-17,共7页
Journal of Southeast University：Natural Science Edition
基金
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
关键词
负参数Mathieu函数
负参数Mathieu导函数
程序包
Mathieu functions with negative parameter
derivative of Mathieu functions with nega-tive parameter
routine package
