%
% Applies a Modified Euler (Runge-Kutta) method to:
%
%   y' = f(y,t)   y(t0)=y0
%
% taking n step sizes of length h.
%
%   w(n+1) = w(n) + h/2 [f(t_n,w_n) + f(t_{n+1},w_n+hf(t_n,w_n))]
%
%
% OUTPUT: vectors (t,Y) where Y(n) is
%         the approximation of y(t) at
%         t(n)=t0+(n-1)*h, n=1,2,3,...
%
%
function [t,w]=ModEul(F,h,n,t0,y0)
 t(1)=t0;
 w(1)=y0;
 for i=2:(n+1)
   k1 = h*feval(F,t(i-1),w(i-1));
   k2 = h*feval(F,t(i-1)+h,w(i-1)+k1);
   w(i)=w(i-1) + (k1 + k2)/2;
   t(i)=t(i-1)+h;
   end