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Zbl 0892.65058
Shirts, Randall B.
Algorithm 721: MTIEU1 and MTIEU2: Two subroutines to compute eigenvalues and solutions to Mathieu's differential equation for noninteger and integer order. (English)
[J] ACM Trans. Math. Softw. 19, No.3, 391-406 (1993). ISSN 0098-3500

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 2000:: *65L15 Eigenvalue problems for ODE (numerical methods)
34B30 Special ODE
34L10 Eigenfunction expansions, etc. (ODE)
34L15 Estimation of eigenvalues for OD operators

Keywords: eigenvalues; eigenfunctions; Mathieu's differential equation; continued fraction techniques

Citations: Zbl 0892.65057

Cited in: Zbl 0892.65057

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