End a Calculation if a condition is satisfied.

I have a calculation to perform:

Part A (Number of iterations are known)

ODE is solved using Runge Kutta 4 and I get an answer

Part B (I dont know the iterations to solve this)

ODE is solved using euler implicit

Condition (Part A-Part B <= 10e-5)

The program should end

Can you help me out with the code ?

[EDITED, Jan, moved from comment section:]

clear all;close all; clc;
format long;
u=1.5;
S=-33;
L=12/100;
N=11;
delx=L/(N-1);

K(1)=0.414;
y(1)=0;
C(1)=0.414;
x(1)=0;

%4th Order RK Method 

for i=1:N-1

x(i+1)=x(i)+delx;
k1 = delx*(S/u*C(i));
k2 = delx*(S/u*C(i)+S/u*k1/2);
k3 = delx*(S/u*C(i)+S/u*k2/2);
k4 = delx*(S/u*C(i)+S/u*k3);   
C(i+1) = C(i) + (1/6)*(k1+2*k2+2*k3+k4);
end
rk4=C(i+1);

N_euler=7839;
for j=1:7839 % i am not supposed to know that the iteration ends here,
it should be dynamic. (When N_euler = 7839, rk4-K(j+1)=10e-5)

%Euler Implicit 

delxeuler=L/(N_euler-1);
y(j+1)=y(j)+delxeuler;
K(j+1)=(K(j)/delxeuler)*(1/((1/delxeuler)-(S/u)));

if abs(rk4-K(j+1))<0.00001
    break

end
end

plot(y,K,'-.+','color','g')
title('Concentration of CO vs. Distance');
xlabel('Axial(x) Direction [m]');
ylabel('Concentration of CO[mol/m3]');
hold on
plot(x,C,'-o','color','r')
legend('Euler Implicit: N=7389','Runge Kutta 4th Order: N=11');

Answer 1

[DIP]

while abs(rk4-imp)>=0.00001
    N_euler = N_euler+1;
    delxeuler=L/(N_euler-1);

      for j=1:N_euler-1
          %Euler Implicit
          y(j+1)=y(j)+delxeuler;
          K(j+1)=(K(j)/delxeuler)*(1/((1/delxeuler)-(S/u)));
          imp=K(j+1);
          err=rk4-imp;
      end

end

Answer 2

[Rik]

The command you are looking for is 'while' instead of 'for'.

So replace the "for j=1:7839" in your code with "while abs(rk4-K(j+1))>0.00001" and you should be golden.

Note: with while loops you have to increment your counter yourself, otherwise your code will loop forever, so add a "j=j+1;" below your while

[DIP]

but K(j+1) is not defined. and will throw an error. Also, how do I define the stepsize delxeuler ?

[Rik]

There are two options:

initialize K before the loop to a value start will result in starting the loop (e.g. K=10^6*rk4),

or you copy the content of the loop, so it runs once before it gets to the while