function compEM
% compEM     Compare Euler and Midpoint for solution of dy/dt = -y;  y(0) = 1
%
% Synopsis:  compEM
%
% Input:     none
%
% Output:    times and global trunc errors for a sequence of stepsizes

tn = 1;  y0 = 1;       %  Length of interval and initial condition

fprintf('\n   h       Time E        errE         Time M        errM\n');
sizes= 2.^-[1:12];
j=1;
for h = sizes
%for h = [0.2  0.1  0.05  0.025  0.0125  0.00625]
  tic;  [te,ye] = odeEuler('rhs2',tn,h,y0);  timee = toc;  %  Euler
  tic;  [tm,ym] = odeMidpt('rhs2',tn,h,y0);  timem = toc;  %  Midpoint
  % --- global discretization errors
  yex = y0*exp(-te);         %  Exact solution at discrete t
  erre = max(abs(ye-yex));   errm = max(abs(ym-yex));            
  fprintf('%8.5f %7d %11.2e %7d %11.2e\n',h,timee,erre,timem,errm);
  times(j,1)=timee;
  times(j,2)=timem;
  errors(j,1)=erre;
  errors(j,2)=errm;
  j=j+1;
end

loglog(sizes, times(:,1), sizes, times(:,2));legend('time e','time m');
figure;
loglog(sizes, errors(:,1), sizes, errors(:,2));legend('error e','error m');
whos