% m28_adaptiveRK.m - examine adaptive time stepping in ODE45

f = @(t,u) u.*tanh(exp(t).*sin(5*t));
LW = 'linewidth'; MS = 'markersize'; FS = 'fontsize';
while 1
   tol = input('tol? (e.g. 1e-2, 1e-4,..., 1e-14) ');  % pick a tolerance
   opts = odeset('reltol',tol,'abstol',tol);
   sol = ode45(f,[0 3],1,opts);                 % ODE45 returns a structure
   tt = linspace(0,3,1000);                     % which we then evaluate
   uu = deval(sol,tt);                          % on a 1000-point grid
   hold off, plot(tt,uu,LW,.6)                  % for plotting
   grid on, hold on
   plot(sol.x,sol.y,'.k',MS,20+0.4*log(tol))    % ODE45's adaptive grid pts
   npts = length(sol.x);                        % the number of these pts
   err = deval(sol,3) - 1.403737560405910;      % error at right-hand BC
   format = 'tol = %3.1e   err = %5.1e   npts = %i';
   s = sprintf(format,tol,err,npts);
   title(s,'fontsize',16)
end