%
% Applies a 2nd order Runge-Kutta method to:
%
%   y' = f(y,t)   y(t0)=y0
%
% taking n step sizes of length h.
%
%   w(n+1) = w(n) + h f(t(n)+h/2,w(n)+h/2*f(t(n),w(n)))
%
%  Specifically,this is the Modified Euler-Cauchy Rule
%  (or the Midpoint Method as it is sometimes called)
%
% INPUT:  F        string variable containing
%                  the name of the function file
%                  where f(t,y) is stored.
%         h        step size
%         n        number of steps 
%         t0       initial value of the t-variable
%         y0       initial value of the y-variable
%          
%
% OUTPUT: vectors (t,w) where w(n) is
%         the approximation of y(t) at
%         t(n)=t0+(n-1)*h, n=1,2,3,...
%
%
function [t,w]=RK(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=feval(F,t(i-1)+h/2,w(i-1)+k1/2);
   w(i)=w(i-1)+h*k2;
   t(i)=t(i-1)+h;
   end