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Re: function writing in differential equations
From: |
Carlo de Falco |
Subject: |
Re: function writing in differential equations |
Date: |
Tue, 14 Oct 2008 20:27:05 +0100 |
On 14/ott/08, at 18:52, genehacker wrote:
xdot(1) = 0.5 * exp(-10*t) - x(4) * x(1);
xdot(2) = x(5) * 0.5 - x(6) * x(2);
xdot(3) = x(6) * x(2) - 0.5 * x(3);
x(4) = 0.5- ((0.5- 0.1)/(1 + (x(1)/5)));
x(5) = 0.5- ((0.5- 0.1)/(1 + (x(1)/5)));
x(6) = 0.1-((0.1- 0.5)/(1 + (x(1)/5)));
put in this form the system is an ODE as you can eliminate x(4:6) in
terms of x(1).
You can solve the system this way:
x4 = @(x1) 0.5- ((0.5- 0.1)/(1 + (x1/5)));
x5 = @(x1) 0.5- ((0.5- 0.1)/(1 + (x1/5)));
x6 = @(x1) 0.1- ((0.1- 0.5)/(1 + (x1/5)));
xdot = @(x,t) [ 0.5 * exp(-10*t) - x4(x(1)) * x(1);
x5(x(1)) * 0.5 - x6(x(1)) * x(2);
x6(x(1)) * x(2) - 0.5 * x(3)];
t = linspace(0,10,100);
x = lsode (xdot, zeros(3,1), t);
plot(t,x)
c.
- function writing in differential equations, genehacker, 2008/10/13
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