MTIEU1

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


References in zbMATH (referenced in 10 articles )

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  1. Erricolo, Danilo; Carluccio, Giuseppe: Algorithm 934, Fortran 90 subroutines to compute Mathieu functions for complex values of the parameter (2013)
  2. Gupta, Sumeet; Poulikakos, Dimos; Kurtcuoglu, Vartan: Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid (2008)
  3. Abramov, A.A.; Kurochkin, S.V.: Calculation of solutions to the Mathieu equation and of related quantities (2007)
  4. Erricolo, Danilo: Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch’s algorithm. (2006)
  5. Volkmer, Hans: Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation (2004)
  6. Aunola, M.: The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials. (2003)
  7. Kokkorakis, G.C.; Roumeliotis, J.A.: Power series expansions for Mathieu functions with small arguments (2001)
  8. Alhargan, Fayez A.: A complete method for the computations of Mathieu characteristic numbers of integer orders (1996)
  9. 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 (1993)
  10. Shirts, Randall B.: The computation of eigenvalues and solutions of Mathieu’s differential equation for noninteger order (1993)