Stopping an Iteration when conditions have been met

Hi guys, im trying to create a loop where I have to compare the euler implicit and RK4 method to compare the accuracy. The implicit method is should stop at 92 iterations to meet the condition where the absolute difference of the solution between the two methods is less than 10e-5.

Thanks !

% Euler’s Implicit Method and RK4
clear;close;clc;
u=1.5;
S=-33;
L=12/100;

N=10000;
delx=L/(N-1);

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

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

A=10;
delx=L/(A-1);

for i=1:inf % Loop for Implicit

%Euler Implicit     
y(i+1)=y(i)+delx;
syms a;
eqn= a ==(K(i)+delx*(a*S/u));
K(i+1) = double(solve(eqn,a));

for i=1:A %loop for RK4

%4th Order RK Method  
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

if abs((C(i+1)-K(i+1)))==0.01
    break
else
    return
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')

Answer 1

[the cyclist]

You are checking for exact equality. Try

if abs((C(i+1)-K(i+1)))<=0.01

instead.

[DIP]

It does not happen sir .

Answer 2

[DIP]

Can anyone suggest to me in general how you dynamically change the iterations ? I want the iteration of the euler implicit to end at 92 iterations.

Answer 3

[Walter Roberson]

You have

for i=1:inf % Loop for Implicit

and within that you have

for i=1:A %loop for RK4

which is using the same variable, i . MATLAB will be able to figure out how to loop properly (it stores the current iteration value internally), but inside that second loop your code is going to be very confused about what i means.

If you want to break at 92 iterations, then change the "inf" to 92.

Also, get rid of that "return"

[DIP]

i want the code to be dynamic , the iteration should end at 92 without me limiting the code to 92 iterations.

[Walter Roberson]

for iter=1:inf % Loop for Implicit

%Euler Implicit     
y(iter+1)=y(iter)+delx;
syms a;
eqn= a ==(K(iter)+delx*(a*S/u));
K(iter+1) = double(solve(eqn,a));

for i=1:A %loop for RK4

%4th Order RK Method  
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

if abs((C(A+1)-K(iter+1))) <= 0.01
    break
end

end