%% A simple example of publishing reports
%% The Euler approximation of the differential equation on [0,2]:
% $$y'+2y=3\exp(-4x),\quad y(0)=1.$$
%% Define the grid size, interval's partition, and the initial value
h=0.1;                       % grid size
x=0:h:2;                     % specify the partition of the interval [0,2]
clear y;                     % clear possibly existing variable y
y(1)=1;                      % initial condition: x1=0, thus y(1) corresponds to y(x1)=1
%% Define the function
f=inline('3*exp(-4*x)-2*y');      
%% Compute the Euler approximation
size(x);                     % size of x to be used in determining the size of vector i
for i=1:20 y(i+1)=y(i)+h*f(x(i),y(i));end  
%% The exact solution
Y_exact=2.5*exp(-2*x)-1.5*exp(-4*x);        
%% The differences between exact and approximate solutions
error = abs(Y_exact-y)'                     
%% Plot of the exact and approximate (dashed curve) solutions
plot(x,y,'--',x,Y_exact)