function [] = prob_2_8( iiMax )
% EX_2_8 - 
% 
% Written by:
% -- 
% John L. Weatherwax                2005-03-10
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

maxError_Eq_2_29 = []; maxError_Eq_2_30 = [];
for ii=2:iiMax,
  h = 2^(-ii);
  nSteps = 2^ii;
  yTruth = exp( -h*(0:nSteps) );

  %
  % Solve using Eq. 2.29:
  %
  % Note: This doesn't seem to agree with the text?  
  % but I couldn't find any errors so ... I'm not 
  % sure where the differences lie...
  ynm2 = exp(-2*h); ynm1 = exp(-h); yn = 1; ys = [ yn ];
  for jj=1:nSteps,
    yp1 = -(1.5+3*h)*yn + 3*ynm1 - 0.5*ynm2;
    ys = [ ys yp1 ];
    ynm2 = ynm1;
    ynm1 = yn;
    yn = yp1;
  end
  
% $$$   figure;
% $$$   plot( -h*(0:nSteps), yTruth, '-g', -h*(0:nSteps), ys, '-r' );

  maxError_Eq_2_29 = [ maxError_Eq_2_29, max( abs(yTruth-ys) ) ];

  %
  % Solve using Eq. 2.30:
  % 
  ynm2 = exp(-2*h); ynm1 = exp(-h); yn = 1; ys = [ yn ];
  for jj=1:nSteps,
    yp1 = (1-(23/12)*h)*yn + (16/12)*h*ynm1 - (5/12)*h*ynm2;
    ys = [ ys yp1 ];
    ynm2 = ynm1;
    ynm1 = yn;
    yn = yp1;
  end
  
% $$$   figure;
% $$$   plot( -h*(0:nSteps), yTruth, '-g', -h*(0:nSteps), ys, '-r' );

  maxError_Eq_2_30 = [ maxError_Eq_2_30, max( abs(yTruth-ys) ) ];
end

% Print the results: 
[ (2:iiMax).', maxError_Eq_2_30.' ]
[ (2:iiMax).', maxError_Eq_2_29.' ]