Summary
The aim of this paper is to propose a fast numerical method for the computation of Mathieu functions. These functions can be used to solve the (reduced) wave equation on an elliptic domain in two space dimensions. In the first part of this paper the theoretical background of the method is discussed, while in the second part the algol procedures are presented.
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References
N. W. McLachlan,Theory and applications of Mathieu functions, Clarendon Press, Oxford, England, 1947.
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions N.B.S.,Applied Mathematical Series 55, U. S. Government Printing Office, Washington D.C., 1964.
G. Blanch, Numerical evaluation of continued fractions,Siam Review 6, p. 383, 1964.
D. J. Green and S. Michaelson, Series solution of certain Sturm Liouville eigenvalue problems,The Computer Journal 7, p. 322, 1965.
J. H. Wilkinson,The algebraic eigenvalue problem, 1965.
Mathematical tables 5, tables 12 and 14, p. 31 and 33.
J. H. Wilkinson, Rigorous error bounds for computed eigensystems.The Computer Journal 4, p. 230.
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The Group “Numerical Analysis” at Delft University of Technology. On the computation of Mathieu functions. J Eng Math 7, 39–61 (1973). https://doi.org/10.1007/BF01535268
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DOI: https://doi.org/10.1007/BF01535268