Algorithm 721: MTIEU1 and MTIEU2
- 1 September 1993
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Mathematical Software
- Vol. 19 (3) , 391-406
- https://doi.org/10.1145/155743.155847
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 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.Keywords
This publication has 4 references indexed in Scilit:
- Computation of the value of the even and odd Mathieu functions of order N for a given parameter S and an argument X [Computer program description]IEEE Transactions on Antennas and Propagation, 1984
- Algorithm 537: Characteristic Values of Mathieu's Differential Equation [S22]ACM Transactions on Mathematical Software, 1979
- Algorithm 352: characteristic values and associated solutions of Mathieu's differential equation [S22]Communications of the ACM, 1969
- Asymptotic Expansions of Mathieu Functions and their Characteristic Numbers.Journal für die reine und angewandte Mathematik (Crelles Journal), 1962