Algorithm 804: subroutines for the computation of Mathieu functions of integer orders

ABSTRACT

Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The routines can handle a large range of the order n and the parameter h. Sample test results and graphs are given.

REFERENCES

• 1: Fayez A. Alhargan, A complete method for the computations of Mathieu characteristic numbers of integer orders, SIAM Review, v.38 n.2, p.239-255, June 1996 [doi>10.1137/1038040]
• 2: ARSCOTT,R.L.AND SHYMANSKY, W. 1978. A three-term recursion and the computation of Mathieu functions. In Proceedings of the 8th Manitoba Conference on Numerical Mathematics and Computing (Manitoba, Canada). 107-115.
• 3: Louis Baker, C mathematical function handbook, McGraw-Hill, Inc., New York, NY, 1992
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• 5: Walter R. Leeb, Algorithm 537: Characteristic Values of Mathieu's Differential Equation [S22], ACM Transactions on Mathematical Software (TOMS), v.5 n.1, p.112-117, March 1979 [doi>10.1145/355815.355824]
• 6: MCLACHLAN, N. 1947. Theory and Applications of Mathieu Functions. Oxford University Press, Oxford, UK.
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INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: C++

Additional Classification:
  G. Mathematics of Computing

General Terms:
Algorithms

Keywords:
Hill's determinant, Mathieu characteristic determinant, Mathieu characteristic numbers, Mathieu coefficients, Mathieu differential equation, Mathieu functions, elliptic coordinates, wave equation