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Timestep change in matlab ballode example
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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
asked Nov 21 '18 at 9:49
sam_rox
4872920
add a comment |
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
differential-equations matlab
asked Nov 21 '18 at 9:49
sam_rox
4872920
add a comment |
0
0
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
differential-equations matlab
asked Nov 21 '18 at 9:49
sam_rox
4872920
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
differential-equations matlab
asked Nov 21 '18 at 9:49
sam_rox
4872920
asked Nov 21 '18 at 9:49
sam_rox
4872920
asked Nov 21 '18 at 9:49
sam_rox
4872920
asked Nov 21 '18 at 9:49
sam_rox
4872920
asked Nov 21 '18 at 9:49
sam_rox
4872920
4872920
add a comment |
add a comment |
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