Vectorization for temperature simulation

I'm new to Matlab and I would like to know tips in order to reduce the processing time of such program. The scheme of the actual code is very similar to typical C++ code and I would like to vectorize the for and if loops in order to decrease the processing time. The code is added just to make you know the overall idea of what I would like to obtain.

close all             %Tanca totes les finestres obertes
clear all             %Removes variables from memory
clc                   %Clears command window
tic                   %inicia comptador temps simulació

trans=fopen('trans_matlab.txt','wt') 

%Physical properties and geometrical data input
Tair=25;
Tinitial=100;
h=10;
k=5;
qv=500;
thick1=0.05;
thick2=0.1;
density=1000;
Cp=800;

%Parameters imput
max_error=0.000001;   %Error màxim a partir del cual no hi ha canvis en els resultats
max_iter=1000000;
r=0.9;
N=10;                 %Nodes paret1          
M=10;                 %Nodes paret2
Inc_x1=thick1/N;
Inc_x2=thick2/M;
num_t=23000;          %temps de realització
Inc_t=20;

%Initial map temperatures
t=1;
for i=1:(N+M+1)       %Hipòtesi inicial: tots els nodes tenen T i Ta = Tair                 
    T(i,t)=Tinitial;      %(N+M+1) pq no deixa començar a 0  
    Ta(i,t)=Tinitial;
end

%GAUS SEIDEL
while t1)&(i(N+1))&(ierrort
            errort=error(i,t);
            else
            errort=errort;
            end
        end
        if errort>max_error
            for i=1:(N+M+1)
                Ta(i,t)=T(i,t).*r+Ta(i,t).*(1-r);
            end
        else
            break
        end
    end
    iter(t)=j;
end

toc
%Print Results
t=1;
fprintf(trans,'time\t T1\t TN+1\t TN+M+1\t iter\n');

while(t<=num_t)
time=t*Inc_t;
fprintf(trans,'%.2f\t %.2f\t %.2f\t %.2f\t %.2f\n',time,T(1,t),T(N+1,t),T(N+N+1,t),iter(t));
t=t+1;
end
fclose(trans);

Besides the hints in comments, I would like to add the following:

-
Replace the abbreviated variables by useful names. This will increase the performance of your code reviewer.

-
Try to keep all your comments in English (see 1.).

-
Preallocate variables if you really want to write their value inside a loop. Even in C++ you would not write Ta(i,t)=Tinitial;.

-
Do you really need all NMnum_t values? If not, you should only store the current and the last iteration.

-
Now try to begin to replace the repetitive statements like Ta(i,t)=T(i,t0); and the sourounding for-loop with a single statement. You don't need to replace all at once.

-
Split your code into a main function and one or more subfunctions. A recent Matlab itself may then increase execution speed of the loops.

-
You calculate c=k/Inc_x1; very often but neither k nor Inc_x1 changes. Try to identify lines which can be computed outside of the loop. Maybe you need to introduce more variables (with good names!).

-
Replace the while-loop by a for-loop. It will be more readable.

-
Correct the indentation of your code. Press Ctrl-A and Ctrl-I.

-
If you have a 2D object, then why not use a 2D array for this. If you really need the results for all times, then you should have a 3D-array. You may then initialize it with temperature = zeros(M, N, T_max);

If you made all this changes, feel free to present your new readable and beautiful code.

StackExchange Code Review Q#77423, answer score: 3