% This matlab script demonstrates the fan of local solutions
% of the DE dy/dx = -y, y(0) = 2, solved by Euler's method
% on [0,1] with a stepsize of 1/4. 
% Usage:    >> fan
% Requires: EulerFixH, dfun

xspan = [0 1]; y0 = 2; nsteps = 4;
[x,y] = EulerFixH('dfun',xspan,y0,nsteps); % Get the computed solution
plot(x,y,'wx',x,y,'r--')                   % Plot as a red dashed line
colors = 'cbmg';
hold on
for k = 1:nsteps
  xloc = linspace(x(k),1);                 % Get each local solution
  yloc = y(k)*exp(-(xloc-x(k)));           %  on a fine mesh
  plot(xloc,yloc,colors(k))                % Plot as a solid line
end
xlabel('X'), ylabel('Y')
title('Computed Solution and Local Solutions Over 4 Steps')