Rb. Shirts, ALGORITHM 721 - MTIEU1 AND MTIEU2 - 2 SUBROUTINES TO COMPUTE EIGENVALUES AND SOLUTIONS TO MATHIEU DIFFERENTIAL-EQUATION FOR NONINTEGER AND INTEGER ORDER, ACM transactions on mathematical software, 19(3), 1993, pp. 391-406
Two FORTRAN routines are described which calculate eigenvalues and eif
enfunctions of Mathieu's differential equation for noninteger as well
as integer order. MTIEU1 uses standard matrix techniques with dimensio
n parameterized to give accuracy in the eigenvalue of one part in 10(1
2). 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.