Defining derivatives in ode45

Hi,

I want to use ode45 to solve a system of ODE as shown below (see the imgae). I am not sure about coding these two equations as I derived them using finite difference method according to the direction. I coded them as:

dydt(1,1) = f(y(1)) + f(y(2));
dydt(2,1) = - (f(y(1)) + f(y(2))); % with -1

The second one was multiplied by -1 to show a countercurrent flow. I am wondeing if this approach is correct. Or I should ignore the negative sign in coding these equations.

dydt(1,1) = f(y(1)) + f(y(2));
dydt(2,1) = (f(y(1)) + f(y(2))); % without -1

Thank you.

[John D'Errico]

Why would you ignore the sign?

[sina]

This is exactly my question! Do I add -1 to show the countercurrent mode? As there is no -1 in original equations.

Answer 1

[David Goodmanson]

Hello sina,

If you turn the diagram around by 180 degrees and then let Ca <--> Cb, you get exactly the same diagram that you started with. That means the equations have to have the same symmetry under Ca <--> Cb. If both equations have a positive sign you do get the same equations. But if one equation has a negative sign, that negative sign switches to the other equation. So positive works, negative doesn't.

Another way of saying the same thing is, starting out with that symmetric diagram, how would you decide which of dCa/dt or dCb/dt gets the negative sign?

[sina]

Hi David,

Thank you for the comment.