i am trying to use ode45 in a system of 4 equations

the problem is about 2 vortexes Q1(x1,y1),Q2(x2,y2)

the equations are :

dx1/dt=Q2*(y1-y2)/l.^2
dy1/dt=-Q2*(x1-x2)/l.^2

dx2/dt=-Q1*(y2-y1)/l.^2
dy2/dt=Q1*(x1-x2)/l.^2

here is my code :

function[d]=lab2(t,IC)
global  Q1 Q2  x1 x2 y1 y2 l
d=zeros(4,1);
d(1)=Q2*(y1-y2)/l.^2;
d(2)=-Q2*(x1-x2)/l.^2;
d(3)=-Q1*(y1-y2)/l.^2;
d(4)=Q1*(x1-x2)/l.^2;
end

i run it on a script :

clear all 
close all
clc
Q1=1
Q2=2
x1=1
x2=-1
y1=0
y2=0
l=2
time_interval=linspace(0,10,200);
initial_contitions=[0 1 0 -1];
[T,Sol]=ode45(@lab2,time_interval,initial_contitions);

it says the following when i try to run it:

In an assignment  A(I) = B, the number of elements in B
and I must be the same.

Error in lab2 (line 4)
d(1)=Q2*(y1-y2)/l.^2;

Error in odearguments (line 87)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1}
to yp0.

Error in ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0,
odeArgs, odeFcn, ...

Error in script (line 13)
[T,Sol]=ode45(@lab2,time_interval,initial_contitions);

i dont know what i m doing wrong...

Answer 1

[Jan]

If I run your code, I do not get an error message. But I've added a defintion of the variables as global in the main program.

But your function to be interagted looks really strange: The derivatrive does neither depend on the time nor on the current values. Then you get an exponential function, which can be solved directly.

Therefore I assume you mean something like this:

function[d]=lab2(t,x)
global  Q1 Q2 l
x1 = x(1);
x2 = x(2);
y1 = x(3);
y2 = x(4);
d  = zeros(4,1);
d(1) =  Q2*(y1-y2)/l.^2;
d(2) = -Q2*(x1-x2)/l.^2;
d(3) = -Q1*(y1-y2)/l.^2;
d(4) =  Q1*(x1-x2)/l.^2;
end