% Approximate solution to Airy BVP
%      y" - x*y = 0, 0 < x < infty
%      y(0) = 1, y(infty) = 0
% using Taylor series approximants about x0 = 0 to two ind. solns
% y0(x) and y1(x) of Airy's equation truncated after term P, and
% replacing infty by xlarge.
% P and xlarge are parameters.specified below by user.
% Because y0(0) = 1 and y1(0) = 0, form of solution is
%   y(x) = y0(x) + c*y1(x), where c is a constant that must be
% determined to satisfy y(xlarge) = 0.


  xlarge = 5;
  Pchoices = [1 3 7 10 30];
  
  x = (0:0.01:1)*xlarge;  % Plotting points; note x(end) = xlarge
  for j = 1:nP
    P = Pchoices(j)
    [y0,y1] = airy_ts(x,P);
    c = -y0(end)/y1(end)
    plot(x,y0+c*y1,[color(j) '-']) % cycle through plot colors
    hold on
    legend_entry(j)= {['P=' int2str(P) ', c=' num2str(c)]}; % j'th cell of a cell array
  end
  hold off
  
  ylim([-1 2])
  xlabel('x')
  ylabel('y^P(x)')
  legend(legend_entry{1:nP},'Location','SouthWest')
  title('Truncated Taylor Series approximants y_0(x) + cy_1(x) to Airy BVP y(0)=1,y(5)=0')