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** Up:** Steady state and boundary
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We want to solve:
Since XPPAUT can only solve systems of first order equations, we
rewrite this as a system of two first order equations:

which translates into the following ODE file

# steady state cable sscab.ode
dv/dt = vx
dvx/dt = v
# boundary condition at left end:
bndry v-1
# boundary condition at right end:
bndry bl*v'+vx'
#
parameter bl=1
done

Since XPPAUT use *t* as its independent variable, we have changed the
name of ``x'' to ``t''. Boundary conditions are set by using the
declaration, `bndry`. XPPAUT will try to set these to zero.
Primes mean to evaluate the variable at the end of the integration
while unprimed variables evaluate at the beginning. To generate these
picture, I just set the total amount for the integration to either of
0.5, 1, 2, 3, corresponding to different electrotonic distances. Then
I used the `Bndry (N)o show` combination to solve the equations.
I used the `Graphics Freeze Freeze` combination to make a
permanent copy of the given curve. I repeated this for each curve and
used the `Text Text` option to draw the text on the curves and the
`View 2d` combination to set the axes and labels.

HOMEWORK

- 1.
- What is the electrotonic length for a cable with
,
- 2.
- Find the input resistance for the semi-infinite cable with the
above parameters
- 3.
- Solve the steady state voltages for
*B*_{L}= 0,.25,1,10,100 on a
cable with electrotonic length 3 using XPPAUT.

** Next:** Equivalent Cylinders
** Up:** Steady state and boundary
** Previous:** Finite cable
*G. Bard Ermentrout*

*1/10/1998*