How to solve 2D Laplace Equation using finite difference method (GUI)

Dear all,

I have problems to solve laplace equation 2d where users can define their own boundaries by drawing up a two-dimensional then matlab should be able to give a solution of laplace equation with a boundary that made earlier and must be able to calculate how many percent about the error that made.

I've made a script but still not right, maybe you can help me .. thank you.

this is my script :

axis([2 20 2 20])
hold on
grid on
xy = [];
n = 0;
but = 1;
while but == 1;
    [xi,yi,but] = ginput(1);
    plot(xi,yi,'ro')
    n = n+1;
    xy(:,n) = [xi;yi];
end

% Plot grafik.
x = round(xy(1,:));
y = round(xy(2,:));
T=zeros(max(x),max(y));
for w=min(x):max(x)-1,   
for q=min(y):max(y)-1,

          T(w,q+1) = w,q+1;
          T(w,q-1) = w,q-1;
          T(w+1,q) = w+1,q;
          T(w-1,q) = w-1,q;

          T(w,q) = (T(w,q+1)+T(w,q-1)+T(w+1,q)+T(w-1,q))/4

end
end
contourf(T,'DisplayName','T');figure(gcf);
plot(x,y,'b-');
hold off;

[Senir Ismail]

try with this script:

n=11; % nodes

l=1.0; % lenght

w=.5; % width

x=linspace(0,l,n);

y=linspace(0,w,n);

T=zeros(n);

% Boundary conditions:

T(n,1:n)=273.0 % Top

T(1,1:n)=273.0 % Bottom

T(1:n,1)=573.0 % left

T(1:n,n)=273.0 % right

eps=1e-6;

error=1;

k=0;

while error>eps

k=k+1

Told=T

for i=2:n-1;

for j=2:n-1;

T(i,j)=.25*(T(i+1,j)+T(i-1,j)+T(i,j-1)+T(i,j+1));

end

end

error=max(max(abs(Told-T)));

end

subplot(2,1,1),contour(x,y,T),colormap,

title('Temperature(steady-state)'),xlabel('x'),ylabel('y'),colorbar;

subplot(2,1,2),pcolor(x,y,T),shading interp,colormap,

title('Temperature(steady-state)'),xlabel('x'),ylabel('y'),colorbar;