Algorithm 721: MTIEU1 and MTIEU2: two subroutines to compute eigenvalues and solutions to Mathieu's differential equation for noninteger and integer order

Authors:
Randall B. Shirts
Affiliations:
-
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1993

Citing 2
Cited 5

Algorithm 537: Characteristic Values of Mathieu's Differential Equation [S22]

ACM Transactions on Mathematical Software (TOMS)
Algorithm 352: characteristic values and associated solutions of Mathieu's differential equation [S22]

Communications of the ACM

Algorithms for the computation of all Mathieu functions of integer orders

ACM Transactions on Mathematical Software (TOMS)
Algorithm 804: subroutines for the computation of Mathieu functions of integer orders

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Algorithm 855: Subroutines for the computation of Mathieu characteristic numbers and their general orders

ACM Transactions on Mathematical Software (TOMS)
Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch's algorithm

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Algorithm 934: Fortran 90 subroutines to compute Mathieu functions for complex values of the parameter

ACM Transactions on Mathematical Software (TOMS)

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Abstract

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 1012. MTIEU2 used continued fraction techniques and is optimized to give accuracy in the eigenvalue of one part in 1014. The limitations of the algorithms are also discussed and illustrated.