refine Subroutine

This procedure calculates the accurate characteristic value
by the secant method.

This routine is copyrighted by Shanjie Zhang and Jianming Jin.  However, 
they give permission to incorporate this routine into a user program 
provided that the copyright is acknowledged.

20 July 2012

Shanjie Zhang, Jianming Jin

Shanjie Zhang, Jianming Jin,
Computation of Special Functions,
Wiley, 1996,
ISBN: 0-471-11963-6,
LC: QA351.C45.

Input, integer ( kind = 4 ) KD, the case code:
1, for cem(x,q)  ( m = 0,2,4,...)
2, for cem(x,q)  ( m = 1,3,5,...)
3, for sem(x,q)  ( m = 1,3,5,...)
4, for sem(x,q)  ( m = 2,4,6,...)

Input, integer ( kind = 4 ) M, the order of the Mathieu functions.

Input, real ( kind = 8 ) Q, the parameter of the Mathieu functions.

Input/output, real ( kind = 8 ) A, the characteristic value, which
should have been refined on output.