TOMS352
Characteristic Values and Associated Solutions of
Matthieu's Differential Equation
TOMS352
is a FORTRAN77 library 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 N1 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 )
Languages:
TOMS352 is available in
a FORTRAN77 version.
Related Data and Programs:
TEST_VALUES,
a FORTRAN77 library which
contains routines which return sample values of various functions,
including the Bessel functions used by this package.
Reference:

Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0486612724,
LC: QA47.A34.

Gertrude Blanch,
Numerical evaluation of continued fractions,
SIAM Review,
Volume 6, Number 4, 1964, pages 383421.

Gertrude Blanch,
Numerical aspects of Mathieu eigenvalues,
Rendiconti Circolo Matematico di Palermo,
Volume 2, Number 15, 1966, pages 5197.

Gertrude Blanch, Donald Clemm,
Tables Relating to the Radial Mathieu Functions,
Volume 1: Functions of the First Kind,
US Government Printing Office, 1962.

Gertrude Blanch, Donald Clemm,
Tables Relating to the Radial Mathieu Functions,
Volume 2: Functions of the Second Kind,
US Government Printing Office, 1962.

Donald Clemm,
Algorithm 352: Characteristic Values and Associated
Solutions of Matthieu's Differential Equation,
Communications of the ACM,
Volume 12, Number 7, pages 399407, June 1969.

Edward Ince,
Tables of the Elliptic Cylinder Functions,
Proceedings of the Royal Society of Edinburgh,
Volume 52, 1932, pages 355423.

Julius Stratton, Philip Morse, Lan Jen Chu, Reina Hutner,
Elliptic Cylinder and Spheroidal Wave Functions,
Wiley, 1941.
Source Code:
Examples and Tests:
List of Routines:

MFCVAL computes the first N characteristic values.

MATH computes solutions of Mathieu's differential
equation.

BOUNDS gets crude upper and lower bounds for the
characteristic values.

MFITR8 improves estimated characteristic values.

TMOFA determines the accuracy of the solution.

COEF computes the neutral coefficients.

SUM_SERIES does series evaluation.

BESSEL evaluates Bessel functions of first or second kind.

J0J1 computes J0(X) and J1(X) for X < 8.

Y0Y1 computes Y0(X) and Y1(X) for X < 8.

LUKE evaluates Bessel functions of order 0 or 1, of the
first or second kind, for 8 <= X.

JNS evaluates Bessel functions of the first kind, given
J0(X) and J1(X).

DS evaluates one term of the radial solution for B(Q).

DC evaluates one term of the radial solution for A(Q).

DDS evaluates one term of the derivative of the
radial solution for B(Q).

DDC evaluates one term of the derivative of the
radial solution for A(Q).

PS evaluates one term of the odd periodic solution.

PC evaluates one term of the even periodic solution.

DPS evaluates one term of the derivative of the
odd periodic solution.

DPC evaluates one term of the derivative of the
even periodic solution.

FJ produces Bessel functions of the first kind.

FY produces Bessel functions of the second kind.

DJ produces derivatives of Bessel functions of the
first kind.

DY produces derivatives of Bessel functions of the
second kind.
You can go up one level to
the FORTRAN77 source codes.
Last revised on 09 October 2006.