clear all
close all

% Problem size and grid spacing, in meters.
Xsize = 1;
DX = 0.25;

% Problem size, in samples.
NX = Xsize/DX + 1;

% Create an axis for output plot.
Xaxis = linspace (0, Xsize, NX);

% Create some space to hold the old guess and new guess.
V_old = zeros(NX,1); 
V_new = zeros(NX,1);

% Establish boundary conditions, V(x=0) = 0, V(x=1) = 1.
V_old(1) = 0;
V_new(1) = 0;
V_old(NX) = 1;
V_new(NX) = 1;

% How many iterations should be done?
max_iterations = 20;

for iteration = 1 : max_iterations
  % This loop doesn't touch the exterior samples, they are unchangeable boundary conditions.
  % ... the interior boundary conditions will the challenging part. You can do it!
  for i = 2 : NX-1
    V_new(i) = 0.5 * ( V_old(i-1) + V_old(i+1) );
  end
  
  % Forget the old guess, overwrite it with the new guess.
  % This prepares us for the next iteration.
  V_old = V_new;
  
  % You don't have to do this, it's just a movie to help you visualize
  figure(1);
  plot (Xaxis, V_new);
  xlabel ('X, meters');
  ylabel ('V(x), Volts');
  title ('Still iterating...');
  set(gcf,'Color',[1 1 1]); % white background
  pause(0.1);
end

% Plot the final converged answer.
figure(2);
plot (Xaxis, V_new);
xlabel ('X, meters');
ylabel ('V(x), Volts');
title ('Solution to Laplace Equation');
set(gcf,'Color',[1 1 1]); % white background
pause(2.0);

% Example "turn-in" plot. (see homework specification)
figure(3);
[x,y] = meshgrid(-2:.2:2, -2:.2:2);
V = x .* exp(-x.^2 - y.^2);
[Ex,Ey] = gradient(V,.2,.2);
contour(x,y,V),hold on, quiver(x,y,Ex,Ey)
title ('Example "turn-in" plot.');
xlabel ('X, meters');
ylabel ('Y, meters');
set(gcf,'Color',[1 1 1]); % white background