WKB , an interactive solution of differential equations using Stokes plots and iterative approach to eigenvalues.
This routine is for solving wkb problems using stokes
methods, the equation is psi"" + q*psi = 0.
to solve a particular problem, the user must
replace the function q with the desired expression
using the frequency dependent coefficients computed
in the subroutine coeff. The real parameters par1
to par6 are available as real physical parameters.
The stokes structure is plotted for the initial
frequency guess, and the frequency plane is iteratively
searched for the eigenvalue connecting selected zeros of q.
as the frequency is moved towards the correct value
the new zeros of q are found and the new stokes
structure plotted.
a,b,c,d,e are complex coefficients in the diff eq
which can depend on frequency.
nstok is the no of points in the stokes plot
z0 is the center of the stokes plot
ranz is the range of the stokes plot
n is the value in integral = (n+.5)*pi
mint is the no. of points in the integral
nsym = 0 implies the code will find the two
turning points independently.
nsym = 1 can be used only if the d.eq. is
symmetric under z to -z and the turning points
selected are symmetrically located about the origin.
nsrh = 0 means the step size in the z-plane search is the
same for both roots, otherwise they can be different
nplt is the no. of iterations between plots of
the frequency plane search and the integrand.
There is also a routine for the numerical integration
of the differential equation.