using the while loop to get the number of divisions

Hi, I am trying to add the while loop to my code such that the code should run while the difference between the present and previous value of Rs is greater than 1e-5 and then record n, the number of times the addition happens and i cant figure out where to add it and how. Below is my code, please help including an alternative way beside the while loop to find n.

f=@(y) 2*pi*(sqrt((y-44.56)/(-0.16))+1)*sqrt(1+((1)/(-0.32*((sqrt((y-44.56)/(-0.16))+1))+0.32))^2);
dt=0.0001;
N=0:dt:40;
Rs=0;
for i=1:numel(N)
    Rs=Rs+f(N(i))*dt;
end

Answer 1

[Rik]

The term you are adding never reaches that low threshold. If it would, the code below would do the trick. You can test it by setting the threshold to something above 4.6e-3

threshold=6e-3;

f=@(y) 2*pi*(sqrt((y-44.56)/(-0.16))+1)*sqrt(1+((1)/(-0.32*((sqrt((y-44.56)/(-0.16))+1))+0.32))^2);
dt=0.0001;
N=0:dt:40;
Rs=0;
R_vec=NaN(size(N));
add_vec=NaN(size(N));
for i=1:numel(N)
    added_term=f(N(i))*dt;
    if abs(added_term)<threshold
        number_of_additions=i-1;
        break
    end
    Rs=Rs+added_term;
    
    R_vec(i)=Rs;
    add_vec(i)=added_term;
end

figure(1),clf(1)
subplot(1,2,1)
plot(N,R_vec),title('value of Rs')
subplot(1,2,2)
plot(N,add_vec),title('\Delta_{iterations}')