function [] = prob_3_8_pt2(Z)
%
% In this implementation we use the derived asymptotic 
% expansions of the solution for large Z as the boundary 
% conditions.  Note that for large Z the decay is so fast
% that a singular Jacobian is encountered.
% 
% Written by:
% -- 
% John L. Weatherwax                2005-04-13
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

P = [ 1 ];
solinit = bvpinit(linspace(0,Z),@guess,P);  
sol = bvp4c(@f,@bcs,solinit,[],Z);
figure; 
p1 = plot( sol.x, sol.y(1,:), '-bo' ); hold on; 
legend( [ p1 ], 'w(z)' ); 
grid on; title( [ 'Z = ', num2str(Z) ] );
%deval(sol,0.1)

function [ v ]  = guess(x)
% GUESS - 
%
v = [ 0.5; 0; ];

function [res] = bcs(ya,yb,P,Z)
% BCS - 
%      
  
res = [ ya(1)-1;
	yb(1)+(P(1)*sqrt(pi)/2)*erfc(Z);
	yb(2)-P(1)*exp(-Z^2);
      ];


function [ ode ] = f(x,y,P,Z)
% F - 
% y(1)=w(z); y(2)=w'(z);
% 

alpha = 0.8; 

ode = [  
    y(2); 
    -( 2*x/sqrt( 1-alpha*y(1) ) )*y(2);
      ];