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Help with Octave for system of ODEs

  1. Dec 10, 2012 #1
    Hi,

    I am having a lot of trouble with Octave as I try to solve a system of ODEs. Any help is appreciated, I am a complete newbie with Octave and numerical solving.

    Let's try a very simple one. Suppose I had a pair of ODEs with a and b being functions of time

    [tex] \frac{da}{dt}=2ba[/tex]
    [tex]\frac{db}{dt}=1[/tex]
    Initial conditions are a(0)=1, b(0)=0

    This is clearly the solved by [tex]a(t)=e^{t^{2}}[/tex] [tex]b(t)=t[/tex] My Octave code was this:

    function xdot=f(x,t);
    xdot=zeros(2,1)
    xdot(1)=2*x(1)*x(2)
    xdot(2)=1
    endfunction

    t=linspace(0,10,100);
    x=lsode("f",[1;0],t)

    I want to plot a(t) against t or b(t) or some combination of a and b against t. Here are my issues

    1) The t=linspace() part. What numbers are appropriate? Sometimes, I got an error saying convergence failure but this combinations worked through blind luck. In general, what should I choose and why does it seem to matter? As I understand, this tells Octave to take t from 0 to 10 and have 100 intervals. I thought any numbers there would have worked?

    2) This is more important. I tried plot(t,x(1)) but I got a blank plot. plot(t,x(2)) also gave me a blank plot. plot(t,x) gave me something but it's really weird. Isn't x now a column vector? I'm not sure what exactly lsode outputs here. What should be the correct command to get a(t) against t, which must of course be an exponential t squared against t graph?

    There's also the fact that when I do it for my actual set of ODEs which are slightly more complicated, it inevitably hits an error or gets something 'x' undefined at a certain column and certain line. I'm quite lost :(

    Thank you for you help.
     
    Last edited: Dec 10, 2012
  2. jcsd
  3. Dec 10, 2012 #2
    Well...don't know ODEs nor Octave, but a quick look at python's scipy revealed a similar function.

    Code (Text):

    import numpy as np
    from scipy.integrate import odeint

    import matplotlib.pyplot as plt

    def dxdt(x,t):
        xdot = np.zeros(2)
        xdot[0] = 2.0*x[0]*x[1]
        xdot[1] = 1.0
        return xdot
       
    t = np.linspace(0,5,51)
    x = odeint(dxdt, [1.0,0.0], t)

    fig = plt.figure()

    ax1 = fig.add_subplot(211)
    ax1.plot(t,x[:,0])
    ax1.set_ylabel('a(t)')

    ax2 = fig.add_subplot(212)
    ax2.plot(t,x[:,1])
    ax2.set_xlabel('t')
    ax2.set_ylabel('b(t)')

    plt.show()

     
    See attached plot, too.
     

    Attached Files:

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