L=ls(F1,F2,a,b,alpha,beta,M)

function L=ls(F1,F2,a,b,alpha,beta,M)

%Input   - F1 and F2 are the systems of first-order equations 
%          representing the I.V.P.'s (9) and (10), respectively
%        - a and b are the endpoints of the interval
%        - alpha = x(a) and beta = x(b); the boundary conditions
%        - M is the number of steps
%Output  - L = [T' X]; where T' is M+1 x 1 vector of abscissas and
%          X is the M+1 x 1 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

Za=[alpha,0];
[T,Z]=rks4(F1,a,b,Za,M);
U=Z(:,1);
Za=[0,1];
[T,Z]=rks4(F2,a,b,Za,M);
V=Z(:,1);
X=U+(beta-U(M+1))*V/V(M+1);
L=[T' X];