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print("Hello World");

%
% Exponent decay
% 'Computational Physics' book by N Giordano and H Nakanishi
% Section 1.2 p2
% Solve the Equation dN/dt = -N/tau
% by Joyful Physics Blog
% ------------------------------------------------------------
<p>N_nuclei_initial = 100; %initial number of nuclei<br />
npoints = 101; % Discretize time into 100 intervals<br />
dt = 0.05; % set time step<br />
tau=1; % set time constant<br />
N_nuclei = zeros(npoints,1); % initializes N_nuclei, a vector of dimension npoints X 1,to being all zeros<br />
time = zeros(npoints,1); % this initializes the vector time to being all zeros<br />
N_nuclei(1) = N_nuclei_initial; % the initial condition, first entry in the vector N_nuclei is N_nuclei_initial<br />
time(1) = 0; %Initialise time<br />
for step=1:npoints-1 % loop over the timesteps and calculate the numerical solution<br />
N_nuclei(step+1) = N_nuclei(step) - (N_nuclei(step)/tau)<em>dt;<br />
time(step+1) = time(step) + dt;<br />
end<br />
% calculate analytical solution below<br />
t=0:0.05:5;<br />
N_analytical=N_nuclei_initial</em>exp(-t/tau);<br />
% Plot both numerical and analytical solution<br />
plot(time,N_nuclei,'ro',t,N_analytical,'b'); %plots the numerical solution in red and the analytical solution in blue<br />
xlabel('Time (s)')<br />
ylabel('Number of nuclei')<br />
text(2,80,'Time constant = 1s')<br />
text(2,70,'Time step = 0.05s')</p>