toms352

toms352, a FORTRAN77 code which implements ACM toms algorithm 352, for determining characteristic values and associated solutions of Matthieu's differential equation.

The text of many ACM toms algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html.

Usage:

The routine MFCVAL computes characteristic values of Mathieu's differential equation:

call mfcval ( n, r, qq, cv, j )
where
input, integer N
the number of characteristic values desired.
input, integer R
given as N-1 or N according as the characteristic values are to be associated with the even or odd solutions, respectively.
input, double precision QQ
the nonnegative parameter.
output, double precision CV(6,N)
the computed array of characteristic values and bounds.
output, integer J
the number of characteristic values successfully computed. If J is not equal to N then an error occurred while trying to compute value J+1.

The routine MATH computes solutions and their derivatives of either Mathieu's differential equation or Mathieu's modified equation, associated with the characteristic values. the Mathieu equation:

call math ( xx, qq, r, cv, sol, fnc, norm, f, k, m )

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

toms352 is available in a FORTRAN77 version.

Related Data and Programs:

toms352_test

test_values, a FORTRAN77 library which contains routines which return sample values of various functions.

Reference:

  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Gertrude Blanch,
    Numerical evaluation of continued fractions,
    SIAM Review,
    Volume 6, Number 4, 1964, pages 383-421.
  3. Gertrude Blanch,
    Numerical aspects of Mathieu eigenvalues,
    Rendiconti Circolo Matematico di Palermo,
    Volume 2, Number 15, 1966, pages 51-97.
  4. Gertrude Blanch, Donald Clemm,
    Tables Relating to the Radial Mathieu Functions, Volume 1: Functions of the First Kind,
    US Government Printing Office, 1962.
  5. Gertrude Blanch, Donald Clemm,
    Tables Relating to the Radial Mathieu Functions, Volume 2: Functions of the Second Kind,
    US Government Printing Office, 1962.
  6. Donald Clemm,
    Algorithm 352: Characteristic Values and Associated Solutions of Matthieu's Differential Equation,
    Communications of the ACM,
    Volume 12, Number 7, pages 399-407, June 1969.
  7. Edward Ince,
    Tables of the Elliptic Cylinder Functions,
    Proceedings of the Royal Society of Edinburgh,
    Volume 52, 1932, pages 355-423.
  8. Julius Stratton, Philip Morse, Lan Jen Chu, Reina Hutner,
    Elliptic Cylinder and Spheroidal Wave Functions,
    Wiley, 1941.

Source Code:

Last revised on 09 November 2023.