Solving 2d laplace equation with insulation ,,,,, code won't work because the error doesn't get below 1 neeeed help

%% 
clear all
close all
clc
%% 
m=7;
n=9;
L=40;
H=30;
dx=L/(n-1);
dy=H/(m-1);

x=0:dx:L;
y=0:dy:H;

lamda=1.5;
epsilon=1e-4;
%% 
T=zeros(m,n);
T_old=zeros(m,n);
%% 
T(:,1)=[120 100 80 60 40 20 0];
T(5:6,9)=[0 0];
%% 
error=1;
iteration=0;
while error>=epsilon
    for j=n-1:-1:2
        for i=2:m-1
            T_old(i,j)=T(i,j);
            T(1,2:4)=(T(1,j+1)+T(1,j-1)+(2*T(2,j)))/4;
            T(1,5)=((2*T(1,4))+(2*T(2,5)))/4;
            T(2:3,5)=(T(i-1,5)+T(i+1,5)+(2*T(i,4)))/4;
            T(4,5)=((2*T(4,4))+(2*T(5,5)))/4;
            T(4,6:8)=(T(4,j+1)+T(4,j-1)+(2*T(5,j)))/4;
            T(7,2:8)=(T(7,j+1)+T(7,j-1)+(2*T(6,j)))/4;
            T(2:4,2:4)=(T(i+1,j)+T(i-1,j)+T(i,j+1)+T(i,j-1))/4;
            T(5:6,2:8)=(T(i+1,j)+T(i-1,j)+T(i,j+1)+T(i,j-1))/4;
            T(i,j)=lamda*T(i,j)+(1-lamda)*T_old(i,j);
            error_T(i,j)=100*abs((T(i,j)-T_old(i,j))/T(i,j));
        end
    end
    error=max(error_T(:));
    iteration=iteration+1;
end
%% 
fprintf('The total number of iterarion is: %d\n',iteration);
fprintf('The temperature values are:\n');
T

Answer 1

[Alan Stevens]

Like this?

m=7;
n=9;
L=40;
H=30;
dx=L/(n-1);
dy=H/(m-1);

x=0:dx:L;
y=0:dy:H;

lamda=1.5;
epsilon=1e-4;
%% 
T=zeros(m,n);
T_old=zeros(m,n);
%% 
T(:,1)=[120 100 80 60 40 20 0];
T(5:6,9)=[0 0];
%% 
error=1;
iteration=0;
while (error>=epsilon) && (iteration<100)
    T_old=T;
    for j=n-1:-1:2
        for i=2:m-1
            T(1,2:4)=(T(1,j+1)+T(1,j-1)+(2*T(2,j)))/4;
            T(1,5)=((2*T(1,4))+(2*T(2,5)))/4;
            T(2:3,5)=(T(i-1,5)+T(i+1,5)+(2*T(i,4)))/4;
            T(4,5)=((2*T(4,4))+(2*T(5,5)))/4;
            T(4,6:8)=(T(4,j+1)+T(4,j-1)+(2*T(5,j)))/4;
            T(7,2:8)=(T(7,j+1)+T(7,j-1)+(2*T(6,j)))/4;
            T(2:4,2:4)=(T(i+1,j)+T(i-1,j)+T(i,j+1)+T(i,j-1))/4;
            T(5:6,2:8)=(T(i+1,j)+T(i-1,j)+T(i,j+1)+T(i,j-1))/4;
        end
    end
    T=lamda*T+(1-lamda)*T_old;
    error_T=100*abs(T-T_old)./T;

    error=max(error_T(:));
    iteration=iteration+1;
end
%% 
fprintf('The total number of iteration is: %d\n',iteration);

The total number of iteration is: 22

fprintf('The maximum error is %g\n', error);

The maximum error is 7.13032e-05

fprintf('The temperature values are:\n');

The temperature values are:

disp(T)

  120.0000   72.6256   72.6256   72.6256   62.5097         0         0         0         0
  100.0000   37.9012   37.9012   37.9012   45.6020         0         0         0         0
   80.0000   37.9012   37.9012   37.9012   45.6020         0         0         0         0
   60.0000   37.9012   37.9012   37.9012   49.2814   51.9268   51.9268   51.9268         0
   40.0000   37.9012   37.9012   37.9012   37.9012   37.9012   37.9012   37.9012         0
   20.0000   37.9012   37.9012   37.9012   37.9012   37.9012   37.9012   37.9012         0
         0   33.3159   33.3159   33.3159   33.3159   33.3159   33.3159   33.3159         0

[Mohammed]

It work but the final answer is wrong The photo shows the right answer

[Torsten]

This is not a MATLAB problem - your discretization must be wrong somehow.

[Mohammed]

It's an assignment in our cours , this is the final answer given to us by our professor and he solve it by matlab.

[Torsten]

Yes, I don't doubt that it can be solved with MATLAB. But your problem is the discretization, not a technical MATLAB issue.

[Mohammed]

Ok thanks my friend i will try and work that out.

[Mohammed]

Ok i worked on my descretizaion and it works thanks for the help much appreciation guys