error: Index in position 2 exceeds array bounds (must not exceed 31).

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
t_max=10;                   %maximum time to get the solution for in sec
delta_t=0.2; 
n_max=(t_max+delta_t)/delta_t;
%Material properties 
alpha=11.234E-05;            %theraml diffusivity
% computional details
i_max=31;                          
j_max=41;
delta_t=0.2;  
delta_x=L/(i_max-1);  
d=alpha*delta_t/(delta_x)^2;  
delta_y=W/(j_max-1); 
%Solution initializing 

T=zeros(j_max,i_max);
T(1,2:i_max-1)= 40;
T(j_max,2:i_max-1)=10;
Tx=T;%taking the initial value
Ty=T;

%processing 

for n=1:t_max     
    for i=2:i_max-1
        for j=2:j_max-1
            TT(i,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 
    end 
    i_max=31;                          
    j_max=41;
    %Boundary conditions 
    TT(j_max,2:i_max-1)=10; %upper
    TT(1,2:i_max-1)= 40; %lower 
    T=TT;
    n=n;
end 

Index in position 2 exceeds array bounds. Index must not exceed 31.

%plottting 
solution_x=0:0.05:L;
solution_y=0:delta_y:W;
T_final = zeros(j_max,length(0:5:i_max));
T_final = T(:,1:5:i_max);
[X,Y] = meshgrid(solution_x,solution_y);
figure(1);
contourf(X,Y,T_final,'linecolor','non')

[Seifeldin Mohamed]

could anyone solve this error !!

Answer 1

[VBBV]

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
t_max=10;                   %maximum time to get the solution for in sec
delta_t=0.2; 
n_max=(t_max+delta_t)/delta_t;
%Material properties 
alpha=11.234E-05;            %theraml diffusivity
% computional details
i_max=31;                          
j_max=41;
delta_t=0.2;  
delta_x=L/(i_max-1);  
d=alpha*delta_t/(delta_x)^2;  
delta_y=W/(j_max-1); 
%Solution initializing 
T=zeros(i_max,j_max);
T(1,2:j_max-1)= 40;
T(i_max,2:j_max-1)=10;
Tx=T;%taking the initial value
Ty=T;
i_max=31;                          
j_max=41;
%Boundary conditions 
TT(i_max,2:j_max-1)=10; %upper
TT(1,2:j_max-1)= 40; %lower 
%processing 
for n=1:t_max     
    for i=2:i_max-1
        for j=2:j_max-1
            TT(i,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));
            T(i,j)=TT(i,j);

        end 
    end 

n=n;
end 
%plottting 
solution_x=linspace(0,L,i_max);
solution_y=linspace(0,W,j_max);
T_final = zeros(i_max,j_max);
T_final = T;
[X,Y] = meshgrid(solution_x,solution_y);
figure(1);
contourf(X,Y,T_final.')
colormap(jet)

[Seifeldin Mohamed]

Thansk, could you expline what was the proeblem ?

[Askic V]

You created initial matrix T in the following way:

T=zeros(j_max,i_max);

which means total number of j_max rows and i_max columns, so 41x31

and yet inside the nested loop at: n = 1, i = 2, j = 31, you tried to use: ...+T(i,j+1)...

that is, you tried to acces the element with indices T(2, 32) which is greater than i_max (31).

[Seifeldin Mohamed]

Thanks , but 0-0.3 should be in the y-axis and 0-0.4 in the x-axis. maybe the porblem in this line

what should I edit in the code ?

[Torsten]

Look at your coding. Clearly, L = 0.3 is the x-extension and W = 0.4 the y-extension.

L=0.3;                      %Length of the The rectangular bar in meter 
W=0.4;                      %Width of the The rectangular bar in meter
% computional details
i_max=31;                          
j_max=41;
delta_x=L/(i_max-1);  
delta_y=W/(j_max-1); 

Maybe the settings here are not as wanted since these values are set left and right, not lower and upper:

TT(i_max,2:j_max-1)=10; %upper
TT(1,2:j_max-1)= 40; %lower 

Answer 2

[Torsten]

Note that I had to make changes to the boundary values and your loop ! Compare with your old code to see the errors you made.

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
t_max=10;                   %maximum time to get the solution for in sec
delta_t=0.2; 
n_max=(t_max+delta_t)/delta_t;
%Material properties 
alpha=11.234E-05;            %theraml diffusivity
% computional details
i_max=31;                          
j_max=41;
delta_t=0.2;  
delta_x=L/(i_max-1);  
d=alpha*delta_t/(delta_x)^2;  
delta_y=W/(j_max-1); 
%Solution initializing 
T=zeros(i_max,j_max);
% Boundary conditions
T(2:i_max-1,1)= 40;
T(2:i_max-1,j_max)=10;
T(1,1) = 40/2;
T(i_max,1) = 40/2;
T(1,j_max) = 10/2;
T(i_max,j_max) = 10/2;
TT = T;
%processing 
for n=1:t_max     
    for i=2:i_max-1
        for j=2:j_max-1
            TT(i,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 
    end 
    T = TT;
end 
%plottting 
solution_x=linspace(0,L,i_max);
solution_y=linspace(0,W,j_max);
T_final = zeros(i_max,j_max);
T_final = T;
[X,Y] = meshgrid(solution_x,solution_y);
figure(1);
contourf(X,Y,T_final.')
colorbar
colormap(jet)

[Seifeldin Mohamed]

thanks

[Torsten]

You know that the correctness of your code heavily depends on delta_x = delta_y ?