# gberg.ode 
# A boundary value problem whose solution represents a 
# rotating spiral wave solution to a two-dimensional partial 
# differential equation.
# z_t = z (1-(1+iq)*z*zbar) + d Del^2 z
#    
#  
init a=0.0118  ap=1.18  k=0  omeg=-0.19  
par d=0.177  q=0.5  sig=3  
# the odes...
a'=ap
ap'=a*k*k-ap/t+a/(t*t)-a*(1-a*a)/d
k'=-k/t-2*k*ap/a-(omeg+q*a*a)/d
omeg'=0
# the boundary conditions
bndry  a-t*ap
bndry  k
bndry  ap'
bndry  k'
# set it up for the user
@ xhi=1 t0=.01,dt=.01,total=.99
done