function  IME=impeuler(f,a,b,ya,h)
% Improved Euler Method that is called Heun Method
%Input    - y'=f is the function 
%            - a and b are the left and right endpoints
%            - ya is the initial condition y(a)
%            - h is the step size
%Output - IME=[T' Y'] where T is the vector of abscissas and
%            - Y is the vector of ordinates

%  NUMERICAL METHODS: Matlab Programs
% (c) 2007 by Xie Liling
%  Complementary Software to accompany the textbook:
%  Information and Computing Science: A Laboratory Course

M=ceil((b-a)/h);
T=zeros(1,M+1);
Y=zeros(1,M+1);
T=a:h:b;
Y(1)=ya;

for j=1:M
   Yj=Y(j)+h*feval(f,T(j),Y(j));
   Y(j+1)=Y(j)+h*(feval(f,T(j),Y(j))+feval(f,T(j+1),Yj))/2;
end

IME=[T' Y'];