Your T_initial is declared as a scalar, you are getting the error when you try to index into it beyond its size. Make that zeros of same size as T. You will find the corrected code below. On a related note, if you want to solve more general problems, check PDE Toolbox Heat Transfer workflow.
Regards,
Ravi
nx=10;
ny=nx;
nt=100;
x=linspace(0,1,nx);
y=linspace(0,1,ny);
dx=x(2)-x(1);
dy=dx;
error=9e9;
tolerance=1e-4;
dt=1e-3;
T_L=0;
T_T=1;
T_R=0;
T_B=0;
T=300*ones(nx,ny);
T(2:ny-1,1)= T_L;
T(2:ny-1,nx)=T_R;
T(1,2:nx-1)=T_T;
T(ny,2:nx-1)=T_B;
T_old= T;
T_initial=zeros(size(T));
k1=1.1*(dt/(dx^2));
k2=1.1*(dt/(dy^2));
Jacobi_iteration=1;
for k= 1:nt
error=9e9;
while(error>tolerance)
for i=2:nx-1
for j= 2:ny-1
Term_1= 1/(1+(2*k1)+(2*k2));
Term_2= k1*Term_1;
Term_3= k2*Term_1;
H= (T_old(i-1,j))+(T_old(i+1,j));
V=(T_old(i,j+1))+(T_old(i,j-1));
T(i,j)= (T_initial(i,j)*Term_1)+ (H*Term_2)+(V*Term_3);
end
end
error=max(max(abs(T_old-T)));
T_old=T;
Jacobi_iteration= Jacobi_iteration+1;
end
T_intial=0;
%Plotting
figure(1)
contourf(x,y,T)
clabel(contourf(x,y,T))
colorbar
colormap(jet)
set(gca,'ydir','reverse')
xlabel('X-Axis')
ylabel('Y-Axis')
title(sprintf('No. of Unsteady Jacobi Iterations(Implicit)=%d', Jacobi_iteration));
pause(0.03)
end
