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Algorithm 721: MTIEU1 and MTIEU2: Two subroutines to compute eigenvalues and solutions to Mathieu’s differential equation for noninteger and integer order. (English) Zbl 0892.65058
Summary: 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 uses 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.

MSC:
65L15Eigenvalue problems for ODE (numerical methods)
34B30Special ODE (Mathieu, Hill, Bessel, etc.)
34L10Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
Software:
MTIEU1