Using ODE45 for coupled equations

Hello,

For the given set of equations, which are coupled, how do I solve them using ODE45 function? I have gone through the documentation for ODE45 but I seem clueless when it comes to this case. Kindly help. I have values for dV/dtheta and dQ/dtheta stored already

Thanks!

[James Tursa]

Looks like you have four variables: P, V, Q, and W. You're going to need four differential equations to solve this. What do you have for dV/dtheta and dQ/dtheta?

[BipityBop]

I have values for dV/dtheta and dQ/dtheta stored already. Sorry, I forgot to mention that

[James Tursa]

Constant values? Or equations?

[BipityBop]

Constant values, for theta ranging from 0 to 360 degrees

[James Tursa]

I don't understand. Do you have equations for dV/dtheta and dQ/dtheta? Why are you suddenly talking about constant values for theta?

[BipityBop]

I have equations for dV/dtheta and dQ/dtheta.

They are as follows

Answer 1

[James Tursa]

General procedure:

Define a variable, let's call it y to match the doc, that will be your state vector. Each element of y corresponds to one of your integration variables. E.g.,

y(1) = P

y(2) = Q

y(3) = V

y(4) = W

y(5) = xb

Then you write a derivative function that calculates the dy/dtheta vector. E.g.,

function dydtheta = myderiv(t,y,g,r,____)  <-- fill in with everything that needs to be passed in
P = y(1);
Q = y(2);
V = y(3);
W = y(4);
Xb = y(5);
dPdtheta = -g * (P/V) * dVdtheta + (g-1)/V * dQdtheta;
dQdtheta = ___;
dVdtheta = ___;
dWdtheta = P * dVdtheta;
dXbdtheta = ___;
dydtheta = [dPdtheta;dQdtheta;dVdtheta;dWdtheta;dXbdtheta];
end

Fill in the blanks with your derivative code.

When you call ode45( ), use a function handle that has all the extra stuff you need to pass in. E.g.,

f = @(t,y) myderiv(t,y,g,r,____);  <-- fill in the extra stuff that needs to be passed in

[BipityBop]

Thanks a ton! Much appreciated