Krdytkyu

In this 'ballode' example of Matlab, which simulates a bouncing ball. Can I please know what the use of this part of the code is?

  % A good guess of a valid first timestep is the length of the last valid

    % timestep, so use it for faster computation.  'refine' is 4 by default.

    options = odeset(options,'InitialStep',t(nt)-t(nt-refine),...

                             'MaxStep',t(nt)-t(1));

particularly, what is the use of t(nt)-t(nt-refine)? How to select the value of refine?

The code works even without this options line, so what is its use?

This is the full code,

function ballode 

%BALLODE Run a demo of a bouncing ball.

% This is an example of repeated event location, where the initial 

% conditions are changed after each terminal event. This demo computes ten 

% bounces with calls to ODE23. The speed of the ball is attenuated by 0.9 

% after each bounce. The trajectory is plotted using the output function 

% ODEPLOT. % % See also ODE23, ODE45, ODESET, ODEPLOT, FUNCTION_HANDLE.

tstart = 0;

tfinal = 30;

y0 = [0; 20];

refine = 4;

options = odeset('Events',@events,'OutputFcn',@odeplot,'OutputSel',1,...

                 'Refine',refine);

figure;

set(gca,'xlim',[0 30],'ylim',[0 25]);

box on

hold on;

tout = tstart;

yout = y0.';

teout = ;

yeout = ;

ieout = ;

for i = 1:10

  % Solve until the first terminal event.

  [t,y,te,ye,ie] = ode23(@f,[tstart tfinal],y0,options);

  if ~ishold

    hold on

  end

  % Accumulate output.  This could be passed out as output arguments.

  nt = length(t);

  tout = [tout; t(2:nt)];

  yout = [yout; y(2:nt,:)];

  teout = [teout; te];          % Events at tstart are never reported. 

  yeout = [yeout; ye];

  ieout = [ieout; ie];

    ud = get(gcf,'UserData');

    if ud.stop

      break;

    end

    % Set the new initial conditions, with .9 attenuation.

    y0(1) = 0;

    y0(2) = -.9*y(nt,2);

    % A good guess of a valid first timestep is the length of the last valid

    % timestep, so use it for faster computation.  'refine' is 4 by default.

    options = odeset(options,'InitialStep',t(nt)-t(nt-refine),...

                             'MaxStep',t(nt)-t(1));

    tstart = t(nt);

  end

plot(teout,yeout(:,1),'ro')

xlabel('time');

ylabel('height');

title('Ball trajectory and the events');

hold off

odeplot(,,'done');

% --------------------------------------------------------------------------

function dydt = f(t,y)

dydt = [y(2); -9.8];

% --------------------------------------------------------------------------

function [value,isterminal,direction] = events(t,y)

% Locate the time when height passes through zero in a decreasing direction

% and stop integration.  

value = y(1);     % detect height = 0

isterminal = 1;   % stop the integration

direction = -1;   % negative direction