Timestep change in matlab ballode example












0














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









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    0














    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









    share|cite|improve this question

























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      0







      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









      share|cite|improve this question













      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






      differential-equations matlab






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      asked Nov 21 '18 at 9:49









      sam_rox

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