T4=taylor(df,a,b,ya,M)

function T4=taylor(df,a,b,ya,M)

%Input   - df=[y' y'' y''' y'''']entered as a string 'df'
%          where y'=f(t,y)
%        - a and b are the left and right endpoints
%        - ya is the initial condition y(a)
%        - M is the number of steps
%Output  - T4=[T' Y'] where T is the vector of abscissas and
%          Y is the vector of ordinates

% NUMERICAL METHODS: MATLAB Programs
%(c) 1999 by John H. Mathews and Kurtis D. Fink
%To accompany the textbook:
%NUMERICAL METHODS Using MATLAB,
%by John H. Mathews and Kurtis D. Fink
%ISBN 0-13-270042-5, (c) 1999
%PRENTICE HALL, INC.
%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
   D=feval(df,T(j),Y(j));
   Y(j+1)=Y(j)+h*(D(1)+h*(D(2)/2+h*(D(3)/6+h*D(4)/24)));
end

T4=[T' Y'];