Coupled set of odes

Hi, I want to solve these coupled set of odes. dy/dt =f1(y)+c1*x; dx/dt =f2(x)+c2*y; Where both x and y are vectors of different size. How to do it using ode45?

Answer 1

[Alan Stevens]

The structure could look something like this

 tspan = [0 tfinal];
 IC = [x0 y0];
 [t, xy] = ode45(@fn, tspan, IC);
 x = xy(:,1);
 y = xy(:,2);

 function dxydt = fn(t,IC)
           c1 = ...;
           c2 = ...;
           x = IC(1);
           y = IC(2);
           f1 = ... (using y);
           f2 = ... (using x);
           dxydt = [f2 + c2*y;
                    f1 + c1*x];
 end

where you would have to fill in with your values of c1, c2 etc.

[Sib RV]

Thank you. I'll try this way.

[Sib RV]

The trouble is, dimensions of x and y are different.'Vectors of different lengths'.

[Alan Stevens]

I took your expressions to mean f1 and f2 were functions (of y and x respectively).

When you say x and y are of different lengths, are you referring to values that represent initial conditions?

[Sib RV]

X and Y are vectors. x1,x2,x3. y1,y2,y3,y4. Real dimensions are around 50. And yes, f1 and f2 are functions of these vectors.

[Alan Stevens]

So what do the functions look like (i.e. their mathematical form); what is the time interval of integration and what are the values of x(t=0) and y(t=0)? And what are the values of c1 and c2?

[Sib RV]

c1 and c2 are constants. F1 and F2 are also similar,constants * (x or y). Like Y'= a y + c x. integration from 0 to arbitrary time.

[Alan Stevens]

If f1 and f2 are aso constants then it becomes even easier. Where I had

           f1 = ... (using y);
           f2 = ... (using x);

you simply put

           f1 = ... ;
           f2 = ... ;

i.e. you specify their values.

Then as long as you have intial values for x and y to go into IC you can integrate up to a time of your choosing.

I don't understand what you mean by having different numbers of x and y values. Do you mean you have values you want to compare the output against?

Do you know the values of f1, f2, c1 and c2, or are you trying to fit them by using x and y data values that you have?

[Sib RV]

I did it this way. x = xy(:,1:length(x)); y = xy(:,length(x)+1:end); And similarly for x and y inside the function fn also. If there is a better suggestion,you are welcome.

Thank you,