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Two FORTRAN routines are described which calculate eigenvalues and eigenfunctions of Mathieu's differential equation for noninteger as well as integer order, MTIEU1 uses standard matrix techniques with dimension parameterized to give accuracy in the eigenvalue of one part in 10 12 . MTIEU2 used continued fraction techniques and is optimized to give accuracy in the eigenvalue of one part in 10 14 . The limitations of the algorithms are also discussed and illustrated.
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Randall B. Shirts (1993) studied this question.
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