% Example: Euler Method calculation of Falling Ball
% Author: F. P. Schloerb
clear
g = 9.8;       % gravitational acceleration
X0 = 0;        % initial values
V0 = 0;
dt = 2;        % step size
t = 0:dt:100;  % array of times for calculation

X = zeros(length(t),1);   % define solution arrays
V = zeros(length(t),1);

% initialize soplution arrays with initial vaulues
X(1) = X0;
V(1) = V0;

% loop to calculate solution
for i=1:length(t)-1
    V(i+1) = V(i) - g*dt;
    X(i+1) = X(i) + V(i)*dt;
end

% make a nice graph of position versus time
plot(t,X,'md')
hold on
plot(t,X0+V0*t-0.5*g*t.*t,'k')
hold off
xlabel('t (s)');
ylabel('X (m)');
legend('Euler Method','Exact')