# Help with Octave for system of ODEs

by McLaren Rulez
Tags: octave, odes
 P: 261 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 $$\frac{da}{dt}=2ba$$ $$\frac{db}{dt}=1$$ Initial conditions are a(0)=1, b(0)=0 This is clearly the solved by $$a(t)=e^{t^{2}}$$ $$b(t)=t$$ 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.
 P: 838 Well...don't know ODEs nor Octave, but a quick look at python's scipy revealed a similar function. 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 Thumbnails

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