[T,Z]=rks4(F,a,b,Za, M)

function [T,Z]=rks4(F,a,b,Za, M)

%Input    - F is the system input as an M-file function
%            - a and b are the endpoints of the interval
%            - Za=[x(a) y(a)] the initial conditions
%            - M is the number of steps
%Output - T is the vector of steps
%            - Z=[x1(t) . . . xn(t)] where xk(t) is the approximation 
%                  to the kth dependent variable

% Call [T,Z]=rksr(@F,a,b,Za,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);
Z=zeros(M+1,length(Za));
T=a:h:b;
Z(1,:)=Za;

for j=1:M
   k1=h*F(T(j),Z(j,:));
   k2=h*F(T(j)+h/2,Z(j,:)+k1/2);
   k3=h*F(T(j)+h/2,Z(j,:)+k2/2);
   k4=h*F(T(j)+h,Z(j,:)+k3);
   Z(j+1,:)=Z(j,:)+(k1+2*k2+2*k3+k4)/6;
end