system of odes

hello i have a system of ode equations i want to solve with ode45. the equations is x1´=s*(x2-x2*x1-x1-q*(x1^2) x2´=(-x2-x1*x2+x3)/s x3´=w*(x1-x3) were s,q and w is constans i also have the conditions x1(0)=30 x2(0)=1 x3(0)=30

i've defined the system of equations in the function fxx,

function yprime=fxx(x,s,q,w) global s; global q; global w; x = zeros(3,1); yprime=[s*(x(2)-x(2)*x(1)-x(1)-q*(x(1)).^2); (-x(2)-(x(1))*x(2)+x(3))/s; w*(x(1)-x(3))]; end

and then i run the command [t,x]=ode45(@fxx,[0 10],[30 1 30]) then i get the errors ??? Error using ==> mldivide Matrix dimensions must agree.

Error in ==> fxx at 4 yprime=[s*(x(2)-x(2)*x(1)-x(1)-q*(x(1)).^2); (-x(2)-(x(1))*x(2)+x(3))/s; w*(x(1)-x(3))];

Error in ==> odearguments at 109 f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ==> ode45 at 173 [neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ... and sometimes i get that x is undefined, im sure i have added the folder to matlab

Answer 1

[Matt Tearle]

The problem is your argument list for fxx. ODE functions should be functions of the independent variable, then the dependent variable, then any other parameters. But you're using global anyway. So... Don't do that. Do this instead

function yprime = fxx(t,x,s,q,w)
% no globals - globals are bad
x = zeros(... etc

Then in your calling script,

s = pi;
q = 42:
w = 1234;
odefun = @(t,y) fxx(t,y,s,q,w);
[t,x] = ode45(odefun,[0,10],[30;1;30]);

[yngv]

after trying your code, x is a vector [30,1,30........30,1,30] which is incorrect, but atleast i dont get any errors :)

maybe the yprime=[...] is wrong? maybe i should use 3 diffrent variables instead of x(1), x(2) and x(3)?

[Matt Tearle]

Oh, waitwaitwaitwaitwait. Didn't read your code carefully enough, sorry.

Delete the line x = zeros(3,1)! What on earth is that doing there? I thought it was preallocating your output (which is yprime, not x -- my bad for not noticing that). x is your input dependent variable. If the first thing you do is overwrite it with zeros, then, yes, not surprisingly, you'll get garbage results.

[yngv]

now it works properly, thank you very much!