%
%   SHOOTA.M    Example of Shooting Method for Solving 2-Point BVPs 
%                      (Automated Iterative Procedure)
%
%   This demo solves a particular 2nd order ODE using an iterative form of
%   the shooting method.  The variable ALF is chosen automatically as part of the 
%   iterative procedure.  This is discussed as Example 5.1 Case 2 Automated 
%   Iteration in the course notes for Math Methods (10/24.539).
%
%   The goal is to find the value of the free parameter, ALF = y'(0) which, 
%   upon solution of the IVP, satisfies the desired boundary condition at x = pi.
%   The automated algortithm for the Shooting Method is imlemented within the
%   BVP2SH.M file.
%
%   also see SHOOTF.M - contains description of given differential equation
%       y'' + 3xy' + 7y  =  cos(2x)     with  y(0) = 1  and  y(pi) = 0
%
%   also see related files:
%       SHOOTM1.M   - solves same problem using a manual iterative scheme
%       SHOOTM2.M   - shows multiple curves of y(x) for different ALF (manual case)
%
%   Files prepared by J. R. White, UMass-Lowell (Aug. 2003)
%

%
%   getting started
      clear all, close all
%
%   set domain limits 
      xo = 0;    xf = pi;    
%
%   set coefficients for BCs
      zbc = [1 0 1.0;      % left BC  --> y(xo) = 1.0
             1 0 0.0];     % right BC --> y(xf) = 0.0
%
%   solution via Shooting Method (numerical approx)
      tol = 1e-6;  options = odeset('RelTol',tol);   % set tight tolerance for ODE soln
      [xs,zs] = bvp2sh('shootf',[xo xf],zbc,options);
%
%   plot final function values 
      plot(xs,zs(:,1),'LineWidth',2),grid
      title('ShootA:  Shooting Method for ODEs (Case 2 - Automated Iteration)')                  
      xlabel('x values'),ylabel('y values')                        
%
%   end demo

