H=heun(f,a,b,ya,M)

function H=heun(f,a,b,ya,M)

%Input    - y'= f is the function 
%            - a and b are the left and right endpoints
%            - ya is the initial condition y(a)
%            - M is the number of steps
%Output - H=[T' Y'] where T is the vector of abscissas and
%            - Y is the vector of ordinates

%If f is defined as an M-file function use the @ notation
% call E=heun(@f,a,b,ya,M).
%If f is defined as an anonymous function use the
% call E=heun(f,a,b,ya,M).

%  NUMERICAL METHODS: Matlab Programs
% (c) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  Upper Saddle River, NJ 07458

h=(b-a)/M;
T=zeros(1,M+1);
Y=zeros(1,M+1);
T=a:h:b;
Y(1)=ya;
for j=1:M
   k1=f(T(j),Y(j));
   k2=f(T(j+1),Y(j)+h*k1); 
   Y(j+1)=Y(j)+(h/2)*(k1+k2);
end

H=[T' Y'];