function A=abm(f,T,Y)

%Input - f is the function entered as a string 'f'
% - T is the vector of abscissas
% - Y is the vector of ordinates
%Remark. The first four coordinates of T and Y must
% have starting values obtained with RK4
%Output - A=[T' Y'] where T is the vector of abscissas and
% Y is the vector of ordinates

% 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

n=length(T);
if n

F=zeros(1,4);
F=feval(f,T(1:4),Y(1:4));
h=T(2)-T(1);

for k=4:n-1
%Predictor
p=Y(k)+(h/24)*(F*[-9 37 -59 55]');
T(k+1)=T(1)+h*k;
F=[F(2) F(3) F(4) feval(f,T(k+1),p)];
%Corrector
Y(k+1)=Y(k)+(h/24)*(F*[1 -5 19 9]');
F(4)=feval(f,T(k+1),Y(k+1));
end

A=[T' Y'];