Numerical Computation of Mathieu Functions

Zhang Shanjie

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Numerical Computation of Mathieu Functions

更新时间：2025-12-08

- Numerical Computation of Mathieu Functions
- Acta Electronica Sinica Issue 9, (1995)
- 作者机构：
  
  1. 南京大学电子科学与工程系
  2. 东南大学生物医学工程系
  3. 南京大学电子科学与工程系东南大学生物医学工程系
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN911.1
- Published：1995
- 稿件说明：
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[1]张善杰,沈耀春.马丢函数的数值计算[J].电子学报,1995(09):41-46.

Zhang Shanjie. Numerical Computation of Mathieu Functions[J]. Acta Electronica Sinica, 1995, (9).
[1]张善杰,沈耀春.马丢函数的数值计算[J].电子学报,1995(09):41-46. DOI：

Zhang Shanjie. Numerical Computation of Mathieu Functions[J]. Acta Electronica Sinica, 1995, (9). DOI：

摘要

本文给出了计算马丢（Ｍａｔｈｉｅｕ）函数和变型马丢函数及其导数值的程序流图和相应的有用数学公式，并讨论了算法。作为典型数值结果，给出了参数ｑ＝±２５时马丢函数、第一类和第二类变型马丢函数前１２阶的函数值及其导数值的数据列表。所编ＦＯＲＴＲＡＮ－７７程序计算精度高，并可适应较宽的参变量范围。

Abstract

Mathieu functions are frequently encountered in many radiation

scattering and guided wave problems

which are formulated in the elliptic cylindrical coordinate system. Mathieu functions are also used in the studies of the elliptic optical fibre waveguides. Consequently their accurate computation is of general importance. A program flowchart for the computation of Mathieu functions and modified Mathieu functions of the first and second kinds

and some useful expressions for numerical computation are presented

and the related algorithms are discussed. Moreover

some typical tabulated data of Mathieu functions of orders up to 12 with positive and negative parameters q are given to eight significant figures.

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