ODE45 wont run, just says "error"?

Hi all, first post here so sorry If I am leaving out details. I am writing an ODE45 file which contains a nested rate function. I've done this numerous times before, but I am getting an error which does not specify where I should look to debug.

Code:

function res = renalclearance()

t_final = 120; %minutes

[T,M] = ode45(@renal_rate, [0,t_final], 10); %10 = initial concentration (mmol/L)

Y = M(:,1);

W = M(:,2);

figure(1) %dci/dt

plot(T,Y)

figure(2) %dce/dt

plot(T,W)

end

function res = renal_rate(t,Z)

Ci = Z(1);

Ce = Z(2);

kc = 0.77; %L/min

kt = 0.25; %L/min

qf = 0.083; %L/min

gi = 0.1; %mmmol/min

v0 = 40; %L

vr = 1.67;

vt = v0-(t*qf);

vi = ((vt)/(1+(1/vr)));

ve = ((vt)/(1+vr));

vdi = 1/(1.598);

vde = 1/(2.67);

dci_dt = -((vdi+kc)*(Ci/vi))+((kc*Ce + gi)/(vi));

dce_dt = -((vde+kc+kt)*(Ce/ve))+((kc*Ci)/(ve));

res = [dci_dt,dce_dt];

end

And here is the corresponding error message:

Error in renalclearance (line 5)

[T,M] = ode45(@renal_rate, [0,t_final], 10); %10 = initial concentration (mmol/L)

Answer 1

[Star Strider]

You have two problems:

First, your system has two differential equations, so you must have two initial conditions:

ic = [0 10];
[T,M] = ode45(@renal_rate, [0,t_final], ic); %10 = initial concentration (mmol/L)

Second, ‘renal_rate’ has to return a column vector:

res = [dci_dt; dce_dt];

Note the vertical concatenation operator here, (;). With these changes your code runs without error. Change the initial conditions (the ‘ic’ vector) if I guessed wrong as to what they should be.

[Nathan Corbissero]

That worked perfectly! Thank you so much.

[Star Strider]

As always, my pleasure!