Re: Second Order ODE

[Ivan Sutoris]

On Mon, Nov 17, 2008 at 7:33 PM, William Christopher Carleton
<address@hidden> wrote:
> I've been trying to get lsode to work on a second order ODE by breaking it 
> into two firsts, but can't seem to figure out the syntax. Does anyone have a 
> code example I could look at?
>
> x'(t)=y(t)
> y'(t)=rx(t)
>
> I was able to code it and get it to plot using a for loop, but I'd really 
> like to see how it could be done with lsode. Thanks,
>
> Chris

If you are trying to solve (d^2 x / d x^2) = r * x, this is how it can be done:

    r = -1;
    x0 = [10; 0];
    t = 0:0.01:10;
    f = @(u,t) [0 1; r 0] * u;
    [X STATE MSG] = lsode(f,x0,t);
    plot(t,X(:,1))

Basically, after transforming to two variables, you get a system

x' = 0*x + 1*y
y' = r*x  + 0*y

so the main trick is to write function f correctly so that it returns
vector [x' ; y'] when you give it vector [x; y] and time t (which is
not used here) as inputs.

Regards
Ivan Sutoris