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# gberg.ode
# A <<real>> boundary value problem whose solution represents a
# rotating spiral wave solution to a two-dimensional partial
# differential equation. There are 3 dynamic variables and
# a free shooting parameter -- omeg --
# Since 4 boundary conditions must be satisfied, there must be 4
# variables and thus the free parameter is treated
# dynamically
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
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