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System of ODE - part III

From: Dennis Bayrock
Subject: System of ODE - part III
Date: Tue, 02 Oct 2001 19:05:34 -0600
User-agent: Mozilla/5.0 (Windows; U; WinNT4.0; en-US; rv:0.9.4) Gecko/20010913


I want to thank everyone again in helping me (particularly Przemek Klosowski!) in helping me to understand Octave's syntax. I am very grateful. With some decifering, I have managed to properly enter my own model consisting of a system of differential-algebraic equations into Octave in order for it to integrate the equations. I am happy to report that it works very well! The results with initial test parameters are precisely what was expected!

Now, is there a way to have Octave determine values for multiple initial constants that are part of my model so that a value from one of the integrated equations can match a specified value? Basically I want to curve fit the resulting plots to my actual experimental data and have Octave determine the best values for the constants that would accomplish this. In the past I have used Excel's SOLVER function to accomplish this task but wish to know if Octave can do the same thing. Again I would humbly ask that someone would give me an actual example that I could enter into Octave so that I can learn by example. As I mentioned before I am not an engineer or a mathematician but would like to learn more about the mathematics in this area of research.

   If a hypothetical example would be of use as a base, then:

function res = f (x, xdot, t)
         res = zeros (3,1);
         res(1) = xdot(1) - D*x(1)*x(2)*xdot(3);
         res(2) = xdot(2) - umax*x(1)*x(3)*xdot(1);
         res(3) = xdot(3) - x(1) - D*xdot(1) - xdot(2);

x0 = [5,50,0]; xdot0 = [0,0,0];

t = linspace (0, 100, 1000);
x = dassl ("f",x0,xdot0,t);
plot (t,x)

   Thanks all in advance!

Dennis Bayrock, P.hD

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