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Defining derivatives in ode45

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sina on 5 May 2019
Commented: sina on 6 May 2019
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
John D'Errico on 5 May 2019
Why would you ignore the sign?
sina on 5 May 2019
This is exactly my question! Do I add -1 to show the countercurrent mode? As there is no -1 in original equations.

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Accepted Answer

David Goodmanson
David Goodmanson on 6 May 2019
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?

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sina on 6 May 2019
Hi David,
Thank you for the comment.

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