Index in position 3 exceeds array bounds (must not exceed 80000).

Hi.

I am trying to modify my Crank Nicholson method code so that it breaks when 14.9<T(11,11,k+1)<15.1 condition is satisfied.

This is the equation

Since time interval is unknown,time variable t, time step variable p and variables including p and t are commented out. I arbitrarily picked p values to obtain the solution but that is not how the code should work. Also whenever I run the code, i got the following error message

Index in position 3 exceeds array bounds (must not exceed 80000).

Error in Crank (line 260)
            T(i,j,k+1)=1/(1+2*r)*(r/2*(T(i-1,j,k+1)+ T(i+1,j,k+1)+ T(i,j+1,k+1)+ T(i,j-1,k+1))+(1-2*r)*T(i,j,k)+r/2*(T(i-1,j,k)+
            T(i+1,j,k)+ T(i,j+1,k)+ T(i,j-1,k)));

How must the code be modified so that it is in an infinite loop and breaks when 14.9<T(11,11,k+1)<15.1 condition is satisfied?

Thanks.

%t=4;                % Total time (s) % Commented out
delta_t=0.05;        % Time step
L=2;                 % Length of each edge
delta_x=0.1;         % Spacing

% Boundary temperatures
T1=10;
T2=10;
T3=10;
T4=10;

% Initial temperature
T5=400;

n=((L/delta_x)+1)^2;    % Total no of nodes
m=sqrt(n);              % Number of nodes in each row and column
%r1=(t/delta_t)+1;       % Number of time steps, commented out
%p=round(r1);            % Number of time steps (rounded)
r=0.033;

% Placing initial and boundary conditions
%T=zeros(m,m,p);         % Pre-allocating

for k=1:80000           % Time-step loop,this line was k=1:p normally 
    for i=1:m           % x coord loop
        for j=1:m       % y coord loop
            if(i==1)&&(j==1)
                T(i,j,k)=(T4+T1)/2;
            elseif(i==1)&&(j==m)
                T(i,j,k)=(T2+T1)/2;
            elseif(i==m)&&(j==m)
                T(i,j,k)=(T2+T3)/2;
            elseif(i==m)&&(j==1)
                T(i,j,k)=(T4+T3)/2;
            elseif(i==1&&(j>1&&j<m))
                T(i,j,k)=T1;
            elseif(j==m&&(i>1&&i<m))
                T(i,j,k)=T2;
            elseif(i==m&&(j>1&&j<m))
                T(i,j,k)=T3;
            elseif(j==1&&(i>1&&i<m))
                T(i,j,k)=T4;
            else
                T(i,j,k)=T5;
            end
        end
    end
end

% Solution

keepgoing = true;
for k=1:80000 % This line was k=1:p normally too
    for i=2:m-1
        for j=2:m-1
            %%%%%%% line 260 below %%%%%%%%%%
            T(i,j,k+1)=1/(1+2*r)*(r/2*(T(i-1,j,k+1)+ T(i+1,j,k+1)+ T(i,j+1,k+1)+ T(i,j-1,k+1))+(1-2*r)*T(i,j,k)+r/2*(T(i-1,j,k)+ T(i+1,j,k)+ T(i,j+1,k)+ T(i,j-1,k)));
            if (i==11 && j==11 && T(11,11,k+1)>14.9 && T(11,11,k+1)<15.1)
             keepgoing =false;
             break;
            end
        end
        if ~keepgoing; break; end
    end
    if ~keepgoing; break; end
end

imagesc(T(:,:,80000));
colorbar;
title('Temperature Profile')

Answer 1

[Torsten]

keepgoing = true;
for k=1:79999 % This line was k=1:p normally too

instead of

keepgoing = true;
for k=1:80000 % This line was k=1:p normally too