# Solve ODE for Parameter Arrays (Python)

* I know this question is pretty simple, but I would like to know the best way to set up such a for loop in Python.

I already wrote a program to calculate and construct a solution to a 2nd order differential equation (this code is shown below).

I would like to know the best techniques for iterating this calculation for an array of f parameters (hence `f_array`

). That is, so the graph shows the `20`

data sets related to solutions as a function of `t`

, each with a different value `f`

.

Cheers for any ideas.

```
from pylab import *
from scipy.integrate import odeint
#Arrays.
tmax = 100
t = linspace(0, tmax, 4000)
fmax = 100
f_array = linspace(0.0, fmax, 20)
#Parameters
l = 2.5
w0 = 0.75
f = 5.0
gamma = w0 + 0.05
m = 1.0
alpha = 0.15
beta = 2.5
def rhs(c,t):
c0dot = c[1]
c1dot = -2*l*c[1] - w0*w0*c[0] + (f/m)*cos((gamma)*t)-alpha*c[0] - beta*c[0]*c[0]*c[0]
return [c0dot, c1dot]
init_x = 15.0
init_v = 0.0
init_cond = [init_x,init_v]
ces = odeint(rhs, init_cond, t)
s_no = 1
subplot(s_no,1,1)
xlabel("Time, t")
ylabel("Position, x")
grid('on')
plot(t,ces[:,0],'-b')
title("Position x vs. time t for a Duffing oscillator.")
show()
```

Here is a graph showing the solution to this equation with respect to a single value `f`

for an array of values `t`

. I would like to quickly repeat this plot for an array of values `f`

.

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Here's one approach:

Modify `rhs`

to accept a third argument, parameter `f`

. The definition `rhs`

must begin

```
def rhs(c, t, f):
...
```

Iterating over `f_array`

with a loop `for`

. In the loop, call `odeint`

with an argument `args`

to `odeint`

give the value `f`

as the third argument `rhs`

. Save the results of each call `odeint`

in a list. Basically replace

```
ces = odeint(rhs, init_cond, t)
```

from

```
solutions = []
for f in f_array:
ces = odeint(rhs, init_cond, t, args=(f,))
solutions.append(ces)
```

For each value `f`

in `f_array`

, you now have a solution listed `solutions`

.

To build them, you can place your call `plot`

in another loop `for`

:

```
for ces in solutions:
plot(t, ces[:, 0], 'b-')
```

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