% matlab_ODE_suite_demo.m

% ode45
% ode23
% ode23s
% ode15s

 clear, home, close all

     y0 = 0.5;
     t0 = 0;
     tFinal = 1.05;
     initialDT = 0.01;
     errorTolerance = 0.0005;
     
     options = odeset('AbsTol',errorTolerance);
    [T,Y] = ode23s(@scalarStiffTestOde,[t0 tFinal],y0,options);
 
   exact = cos(T) + (y0 - 1)*exp(-100*T);
   norm(Y(:,1)-exact,inf)
   plot(T,Y(:,1),'b-o',T,exact,'r','MarkerSize',4)
   hold on
   plot(T,exact,'r')
   plot(T,0.45*ones(1,length(T)),'k.')
   hold off
   
   axis([t0-0.05 tFinal 0.4 1.05])
   title 'Matlab ODE suite'
   
   disp('steps: ')
   length(T)