% Example: Euler Method for Radioactive Decay
% Author: F. P. Schloerb
clear

k = 0.05;         % decay constant
N0 = 1000;        % initial value
dt = 1;           % step size
t = 0:dt:100;     % array of times for calculation

N = zeros(length(t),1);   % define solution array

% Main Loop to calculate N for all times t
N(1) = N0;
for i=1:length(t)-1
    N(i+1) = N(i) - k*N(i)*dt;
end

% make some nice graphs
plot(t,N,'md')            % the numerical solution
hold on
plot(t,N0*exp(-k*t),'k')  % the exact solution
hold off
xlabel('t');
ylabel('N');
legend('Euler Method','Exact')