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

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

%Input    - F is the system input as a string 'F'
%         - 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

% 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);
Z=zeros(M+1,length(Za));
T=a:h:b;
Z(1,:)=Za;

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