How do you sum concatenated variables in a system of ODES with a For Loop?

N = 3
% custom MATLAB function containing ODES
function dCdt = model(t,C,N)
    % Inner Parameters
    A = 3;
    B = 2;
    h = 10/N
    % ODE system initialization
    dCdt = zeros(N,1);
    
    K1 = 0;
    K2 = C(1)*A + B;
    K3 = C(2)*A + B;
    
    sumK = K2 + K3;
    
    % ODES
    
    dCdt(1) = 0;
    dCdt(2) = -((C(2)-C(1))/h) + K2/sumK;
    dCdt(3) = -((C(3)-C(2))/h) + K3/sumK;

end

Above you can see a static example of an ODE system with three ODEs. However, I want to automate this function so It can handle any number ("N") of ODEs. I have not found a way to include a For Loop inside the function that not only updates the number of ODEs but also the lengh of the "K" summation. Since the first ODE will always be equalt to zero, I can easialy run a for loop to define ODES from 2 to N. But, How would I write an expression that also update the concatenated summation term for any "N" value?

Thank you for your time and support!

[Jan]

Hint: The "k3" should be "K3" (upper case) I assume.

[Roger Vegeta]

Yes!

Answer 1

[Davide Masiello]

This should do it for any N

N = 3;
[t,X] = ode45(@(t,C)model(t,C,N),[0,2],rand(1,N));
plot(t,X)
legend('c1','c2','c3')

function dCdt = model(t,C,N)
% Inner Parameters
A = 3;
B = 2;
h = 0.1;  % <-- added a values for h

% ODE system initialization
dCdt = zeros(N,1);
K    = zeros(N,1);

K(2:end) = C(1:end-1)*A + B;

sumK = sum(K(2:end));

dCdt(2:end) = -((C(2:end)-C(1:end-1))/h) + K(1)/sumK;
end

[Roger Vegeta]

This looks neat, let me try it first!

[Davide Masiello]

Check latest edit, I had found a bug :)

[Roger Vegeta]

sorry, the edits were to fix some K terms and add an "h" parameter

[Davide Masiello]

yes I noticed that h was missing, so I edited again adding an arbitrary value.

I also run the code for some initial conditions I made up.

Obviously, C1 will be constant, since its derivative is zero.

[Roger Vegeta]

Awesome! Thank you so much this works!

[Davide Masiello]

Anytime ;)

Answer 2

[Jan]

This is trivial, if you do not create a bunch of variables, but an array:

    K(1) = 0;
    K(2) = C(1) * A + B;
    K(3) = C(2) * A + B;
    ...
    sumK = sum(K);
    

Or without a loop:

K = C * A + B;

If K1 is 0, the last term of the ODEs will vanish in all cases, so simply omit it.

[Roger Vegeta]

good observations!