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) 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 07458Za=[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];