% Compute and plot the results of a fd code on a simple grid
J = 4; N = 8;
T = 0.2;
x = linspace(0,1,J+1);
t = linspace(0,T,N+1);
u = zeros(j+1,n+1); h=zeros(J+1,N+1);
% plot the grid
figure(1),clf
axis off
hold on
for j=1:J+1
  line(repmat(x(j),1,N+1),t,'color','k')
end

for n=1:N+1
  line(x,repmat(t(n),1,J+1),'color','k')
end

for j=1:J+1
  line(x(j),t(1),'marker','o','markerfacecolor','r','markeredgecolor','k','markersize',5)
end

for n=2:N+1
  line(x(1),t(n),'marker','o','markerfacecolor','r','markeredgecolor','k','markersize',5)
  line(x(end),t(n),'marker','o','markerfacecolor','r','markeredgecolor','k','markersize',5)
end

for j=2:J
  for n=2:N+1
    line(x(j),t(n),'marker','o','markerfacecolor','b','markeredgecolor','k','markersize',5)
  end
end
drawnow
pause

pos = get(gca,'position');
for j=1:J+1
  for n=1:N+1
    h(j,n) = annotation('textbox',...
      [pos(1)+(x(j)-0.05)*pos(3),pos(2)+(t(n)/T-0.075)*pos(4),...
      0.1*pos(3),0.06*pos(4)]);
    set(h(j,n),'backgroundcolor',0.8*[1 1 1],...
      'horizontalalignment','center','verticalalignment','middle')
    set(h(j,n),'string','')
  end
end
drawnow
pause
% Now perform an explicit finite difference computation.
% Set the boundary values
nu = T*J^2/N;
for j=1:J+1
  u(j,1) = x(j)^2;
  set(h(j,1),'string',sprintf('%5.3f',u(j,1)))
end
for n = 2:N+1
  u(1,n) = 0;
  u(J+1,n) = 1;
  set(h(1,n),'string',sprintf('%5.3f',u(1,n)))
  set(h(J+1,n),'string',sprintf('%5.3f',u(J+1,n)))
end
drawnow
pause
% Loop through time and across the grid
for n=2:N+1
  for j=2:J
    set(h(j,n),'backgroundcolor','w')
    set(h(j-1,n-1),'backgroundcolor','w')
    set(h(j,n-1),'backgroundcolor','w')
    set(h(j+1,n-1),'backgroundcolor','w')
    pause(0.5)
    u(j,n) = (1-2*nu)*u(j,n-1)+nu*(u(j-1,n-1)+u(j+1,n-1));
    set(h(j,n),'string',sprintf('%5.3f',u(j,n)))
    pause(0.5)
    set(h(j,n),'backgroundcolor',0.8*[1 1 1])
    set(h(j-1,n-1),'backgroundcolor',0.8*[1 1 1])
    set(h(j,n-1),'backgroundcolor',0.8*[1 1 1])
    set(h(j+1,n-1),'backgroundcolor',0.8*[1 1 1])
  end
  % impose a zero-derivative condition at the RHS
  set(h(J+1,n),'backgroundcolor','w')
  set(h(J,n-1),'backgroundcolor','w')
  set(h(J+1,n-1),'backgroundcolor','w')
  pause(0.5)
  u(J+1,n) = (1-nu)*u(J+1,n-1)+nu*u(J,n-1);
  set(h(J+1,n),'string',sprintf('%5.3f',u(J+1,n)))
  pause(0.5)
  set(h(J+1,n),'backgroundcolor',0.8*[1 1 1])
  set(h(J,n-1),'backgroundcolor',0.8*[1 1 1])
  set(h(J+1,n-1),'backgroundcolor',0.8*[1 1 1])
end