MATLAB question regarding loop

if true
clc;
clear;
FL=0.04;        %Fin length
BL=0.005;       %Base length
TL=BL+FL;       %Total length
FW=0.010;       %Fin width 
BW=0.030;       %Base width
dx=0.001; 
dy=dx;
%Total Nodes
M=round(((BW/2)/dx+1));  %i Direction
N=round(((TL)/dx+1));    %j Direction
%Initial Temperature
T=zeros(M,N);
loop=10000;              %Number of Iterations
err_max = 1e-6;          %Maximum Error
n=0; %Number of Iterations
while n<loop
  n=n+1; 
  Tp=T; 
  for i=1:1:M
      for j=1:1:N

           %Corner Node 8 
           if i==1 & j==1 %(i=0, j=0)
             T(i,j)=(1/2)*(T(i,j+1)+T(i+1,j))+(7500/89)*dx;

           %Corner Node 13
           elseif i==M & j==1 %(i=15, j=0)
             T(i,j)=(1/2)*(T(i,j+1)+T(i-1,j))+(7500/89)*dx;

           %Corner Node 9
           elseif i==1 & j==N %(i=0, j=45)
             T(i,j)= (89*(T(i+1,j)+T(i,j-1))+4500*dx)/(150*dx+178);

           %Constant heat flux boundary node 5
           elseif i>1 & i<M & j==1 %(i=1 to 14, j=0)
             T(i,j)=(1/4)*(T(i-1,j)+T(i+1,j))+(1/2)*(T(i,j+1))+(7500/89)*dx; 

           %Symmetrical boundary node 2  
           elseif i==1 & j>1 & j<N %(i=1 , j=1 to 45)
             T(i,j)=(1/4)*(T(i,j+1)+T(i,j-1))+(1/2)*(T(i+1,j));

           %Convective boundary node 7  
           elseif i>1 & i<6 & j==N  %(i=1 to 4 , j= 45)
             T(i,j)=((89)*(T(i-1,j)+T(i+1,j))+(178)*(T(i,j-1))+9000*dx)/(300*dx+356);

           %Convective Corner Node 10  
           elseif i==6 & j==N  %(i=5 , j= 45)
             T(i,j)=((89)*(T(i-1,j)+T(i,j-1))+9000*dx)/(300*dx+178);

           %Convective Boundary Node 3  
           elseif i==6 & j>5 & j<N  %(i=5, j= 5 to 44)
             T(i,j)=((89)*(T(i,j+1)+T(i,j-1))+178*T(i-1,j)+9000*dx)/(9000*dy+356); 

           %Corner Node 11  
           elseif i==6 & j==6   %(i=5, j=5)
             T(i,j)=((178)*(T(i-1,j)+T(i,j-1)+T(i+1,j)+T(i,j+1))+4500*dy)/(150*dy+534);

           %Corner Node 12  
           elseif i==M & j==6   %(i=15, j=5)
             T(i,j)=((89)*(T(i-1,j)+T(i,j-1))+4500*dx)/(150*dx+178);  

           %Convective Boundary Node 6  
           elseif i>5 & i<M & j==6   %(i=5 to 15, j=5)
             T(i,j)=((178)*(T(i,j-1))+(89)*(T(i+1,j)+T(i-1,j))+9000*dx)/(9000*dx+356);  

           %Symmetrical Boundary Node 4  
           elseif i==M & j>1 &j<6   %(i=15, j=1 to 4)
             T(i,j)=(1/4)*(T(i,j-1)+T(i,j+1))+(1/2)*(T(i-1,j));  

           %Internal Node 1 (SOLID)
           elseif i>1 & i<M & j>1 & j<6
             T(i,j)=(1/4)*(T(i,j-1)+T(i,j+1)+T(i+1,j)+T(i-1,j));

           %Internal Node 1 (SOLID)
           elseif i>1 & i<6 & j>5 & j<N
             T(i,j)=(1/4)*(T(i,j-1)+T(i,j+1)+T(i+1,j)+T(i-1,j));   

            end;
            err = max(abs(T - Tp))
        end
end
if err < err_max
break   
end
end
  end

Answer 1

[Image Analyst]

Lots wrong with that code. Gladd to see that you're using a failsafe (limit to number of iterations though). Here, just try this. I fixed several things.

FL=0.04;        %Fin length
BL=0.005;       %Base length
TL=BL+FL;       %Total length
FW=0.010;       %Fin width
BW=0.030;       %Base width
dx=0.001;
dy=dx;
%Total Nodes
M=round(((BW/2)/dx+1));  % i Direction
N=round(((TL)/dx+1));    % j Direction
%Initial Temperature
T=zeros(M,N);
maxLoopIterations = 10000;              % Number of Iterations
err_max = 1e-6;   % Maximum Error
n=0; %Number of Iterations
err = zeros(1, maxLoopIterations);
while n < maxLoopIterations
  n=n+1;
  Tp=T;
  for i=1:1:M
    for j=1:1:N
      %Corner Node 8
      if i==1 && j==1 %(i=0, j=0)
        T(i,j)=(1/2)*(T(i,j+1)+T(i+1,j))+(7500/89)*dx;
        
        %Corner Node 13
      elseif i==M && j==1 %(i=15, j=0)
        T(i,j)=(1/2)*(T(i,j+1)+T(i-1,j))+(7500/89)*dx;
        
        %Corner Node 9
      elseif i==1 && j==N %(i=0, j=45)
        T(i,j)= (89*(T(i+1,j)+T(i,j-1))+4500*dx)/(150*dx+178);
        
        %Constant heat flux boundary node 5
      elseif i>1 && i<M && j==1 %(i=1 to 14, j=0)
        T(i,j)=(1/4)*(T(i-1,j)+T(i+1,j))+(1/2)*(T(i,j+1))+(7500/89)*dx;
        
        %Symmetrical boundary node 2
      elseif i==1 && j>1 && j<N %(i=1 , j=1 to 45)
        T(i,j)=(1/4)*(T(i,j+1)+T(i,j-1))+(1/2)*(T(i+1,j));
        
        %Convective boundary node 7
      elseif i>1 && i<6 && j==N  %(i=1 to 4 , j= 45)
        T(i,j)=((89)*(T(i-1,j)+T(i+1,j))+(178)*(T(i,j-1))+9000*dx)/(300*dx+356);
        
        %Convective Corner Node 10
      elseif i==6 && j==N  %(i=5 , j= 45)
        T(i,j)=((89)*(T(i-1,j)+T(i,j-1))+9000*dx)/(300*dx+178);
        
        %Convective Boundary Node 3
      elseif i==6 && j>5 && j<N  %(i=5, j= 5 to 44)
        T(i,j)=((89)*(T(i,j+1)+T(i,j-1))+178*T(i-1,j)+9000*dx)/(9000*dy+356);
        
        %Corner Node 11
      elseif i==6 && j==6   %(i=5, j=5)
        T(i,j)=((178)*(T(i-1,j)+T(i,j-1)+T(i+1,j)+T(i,j+1))+4500*dy)/(150*dy+534);
        
        %Corner Node 12
      elseif i==M && j==6   %(i=15, j=5)
        T(i,j)=((89)*(T(i-1,j)+T(i,j-1))+4500*dx)/(150*dx+178);
        
        %Convective Boundary Node 6
      elseif i>5 && i<M && j==6   %(i=5 to 15, j=5)
        T(i,j)=((178)*(T(i,j-1))+(89)*(T(i+1,j)+T(i-1,j))+9000*dx)/(9000*dx+356);
        
        %Symmetrical Boundary Node 4
      elseif i==M && j>1 &&j<6   %(i=15, j=1 to 4)
        T(i,j)=(1/4)*(T(i,j-1)+T(i,j+1))+(1/2)*(T(i-1,j));
        
        %Internal Node 1 (SOLID)
      elseif i>1 && i<M && j>1 && j<6
        T(i,j)=(1/4)*(T(i,j-1)+T(i,j+1)+T(i+1,j)+T(i-1,j));
        
        %Internal Node 1 (SOLID)
      elseif i>1 && i<6 && j>5 && j<N
        T(i,j)=(1/4)*(T(i,j-1)+T(i,j+1)+T(i+1,j)+T(i-1,j));
        
      end
    end
  end
  diffMatrix = abs(T - Tp);
  err(n) = max(diffMatrix(:));
  if err(n) < err_max
    break
  end
end
% Crop off unused part of array
err = err(1:n);
plot(err, 'b-', 'LineWidth', 2);
grid on;
drawnow;
fontSize = 20;
title('Error vs. Iteration Number', 'FontSize', fontSize);
xlabel('Iteration Number', 'FontSize', fontSize);
ylabel('Error', 'FontSize', fontSize);
xticks(0:100:n);
yticks(0:.01:.15);

Answer 2

[Wick]

In general, when inside a loop you can keep track of "something" simply by assigning that value to an element in a vector using the index of the loop to place the value. Example:

 loop_length = 10000;
 error_vector = zeros(1,loop_length)
 for jj = 1:loop_length
      error_vector(jj) = abs(10000 - jj);
 end

Obviously, this is an inefficient way to go about defining the error_vector as I've written but it gives you an idea of how you might use the loop index to assign a value to a position in a vector.