function [y,t] = forwardEuler(y0,tfinal,nsteps)
% function [y,t] = forwardEuler(y0,tfinal,nsteps)
%
% Forward Euler for nonlinear equations
%
% This function uses Forward Euler to solve
%   y' = f(t,y)
%   y(0) = y_0
% That is, for n = 1,2,3, ...
%   y_{n+1} = y_n + (t_{n+1} - t_n)f(t_n,y_n)
%
% We assume that an m-file function f.m exists for computing f: [ff] = f(t,y).
%
% Inputs:
%   y0        The initial condition (either a row or column vector).
%   tfinal    The final time.
%   nsteps    The number of steps to take.
% Outputs:
%   y         The solution.
% Internal Variables:
%   dt        The time step.
%   n         The time step number.
%   t         The current time.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Checking of inputs
%
if tfinal <= 0
  y = y0;
  return;
end
if nsteps <= 0
  nsteps = 1;
end
%
% Initialization
%
dt = tfinal/nsteps;
y(1) = y0;
t(1) = 0;
%
% Time step loop
%
for n = 1:nsteps
  y(n+1) = y(n) + dt*f(t(n),y(n));
  t(n+1) = t(n) + dt;
end
return;