While I am running this code I get this error, could anyone knows how to solve it ? (Unable to perform assignment because the size of the left side is 1-by-41 and the size of)

clear all
clc
%Geometry definition
L=0.3;                      %Length of the The rectangular bar in meter 
W=0.4;                      %Width of the The rectangular bar in meter
%Material properties 
alpha=11.234E-05;            %theraml diffusivity
% computional details
x_min=0;
y_min=0;
i_max=31;                          
j_max=41;
delta_t=0.2;  
t_max=10;                   %maximum time to get the solution for in sec
n_max=length(0:delta_t:t_max);
delta_x=L/(i_max-1); 
delta_y=W/(j_max-1); 
d=alpha*delta_t/(delta_x)^2;   


%Solution initializing 
M1_store_x=zeros(j_max,i_max,n_max);  %3d matrix to save time data for i
M2_store_y=zeros(j_max,i_max,n_max);  %3d matrix to save time data for j
T=zeros(i_max,j_max);
%Boundary conditions 
T(i_max,:)=10; %upper
T(1,:)=40; %lower 
T(:,j_max)=0.0; %right 
T(:,1)=0.0; % left
Tx=T;
Ty=T;
%Initial conditions 

for i=2:30;
    for j=2:40;
        T(i,j)=0;
    end 
end 

%processing 
%loop for x sweep
for n=1:n_max    
    b_vec=zeros(i_max,1);
    b_vec(1,1)=0;
    b_vec(i_max,1)=0;
    for j=2:j_max-1
        for i=2:i_max-1
            b_vec(i)=T(i,j)+d*(T(i-1,j)+T(i+1,j)+T(i,j-1)+T(i,j+1)-4*T(i,j));
        end
        ut =b_vec;
        Tx(j,:)=ut;
        %storing the values in 3D matrix
        M1_store_x(:,:,n)=Tx;
    end 
    %-------------------y sweep--------------
    %declaring the vector
    b_vec=zeros(ny,1);
    b_vec(1,1)=40;
    b_vec(ny,1)=10;
    for i = 2:i_max-1
        for j = 2:j_max-1
            b_vec(j)=T(i,j)+d*(T(i-1,j)+T(i+1,j)+T(i,j-1)+T(i,j+1)-4*T(i,j));
        end 
        ut1 = b_vec;
        Ty(:,i)=ut1;
    end 
    M2_store_y(:,:,k)=Ty;
end 
%plotting 
solution_x=0:0.05:L;
solution_y=0:dy:W;
T_final = zeros(j_max,length(0:5:i_max));
s=1;
for k=1:5:i_max
    T_final(:,s)= M2_store_y(:k,10);

Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To construct matrices, use brackets instead of parentheses.

    s=s+1;
end
figure(1);
[xx,yy]= meshgrid(solution_x,solution_y);
mesh(xx,yy,T_final)
title('10 s Solution of FTCS Method')
xlabel('W')
ylabel('L')
zlabel('Temperatur(ºC)')

[Walter Roberson]

T_final(:,s)= M2_store_y(:k,10);

The :k part is not valid.

Have you considered replacing the entire loop with

T_final = M2_store_y(:, 1:5:i_max, 10);

... if I am guessing correctly what your code is intended to do.

[Seifeldin Mohamed]

the problem occurs in the %processing section !!

[Walter Roberson]

You cannot get to the %processing section until the syntax error is fixed in the %plotting section.

[Seifeldin Mohamed]

I am checking each section by evaluate selection and I get the error in the %processing section !!. could you please check this section. Please

Answer 1

[Walter Roberson]

b_vec=zeros(i_max,1);

That is a column vector

    b_vec(1,1)=40;
    b_vec(ny,1)=10;
    for i = 2:i_max-1
        for j = 2:j_max-1
            b_vec(j)=T(i,j)+d*(T(i-1,j)+T(i+1,j)+T(i,j-1)+T(i,j+1)-4*T(i,j));
        end

Stays a column vector

        ut =b_vec;

ut is assigned the column vector

        Tx(j,:)=ut;

The column vector is assigned to a row of Tx.

Assigning a column vector to a row is legal in MATLAB. The problem is that the column vector has the same number of elements as there are rows in Tx, rather than having the same number as there are columns in Tx.