Re: function writing in differential equations

[Carlo de Falco]

On 14/ott/08, at 20:27, Carlo de Falco wrote:

> 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.


BTW if for some reason you still wish to use DASSL (or DASPK) for  
solving the system above, you can do:

f = @(x,xprime,t) ( xprime - xdot(x,t));
X = daspk (f, zeros(3,1), xdot(zeros(3,1),0), t);

which of course gives the same result as you can see by doing

plot(t,x,t,X,'kx')

c.