Does event location terminate ODE solver at tspan?

I just wonder what's the behavior of this edge case: a event location is setup to terminate the intergration, however the event coincide with the end of tspan.

options = odeset('Events',@myEventsFcn)
[t,y,te,ye,ie] = odeXY(odefun,tspan,y0,options)
function [value,isterminal,direction] = myEventsFcn(t,y)
...
isterminal=1;
end

If value(1) becomes 0 exactly on t==tspan(end)

Will te,ye,ie contain values, or be empty in this case?

Answer 1

[Harsh Sharma]

Hi Yi-xia Liu,

The values of variables “te”,”ye” and “ie” are empty when the event is set to terminate the integration at “t=tspan(end)”. I have created an example to verify this for which the code is provided below:

function ballode2 
tstart = 0; 
tfinal = 4; 
y0 = [0; 20]; 
refine = 4; 
options = odeset('Events',@events,'OutputFcn',@odeplot,'OutputSel',1,... 
    'Refine',refine); 
fig = figure; 
ax = axes; 
ax.XLim = [0 5]; 
ax.YLim = [0 25]; 
box on 

hold on; 
tout = tstart; 
yout = y0.'; 
teout = []; 
yeout = []; 
ieout = []; 
   % Solve until the first terminal event. 
   [t,y,te,ye,ie] = ode23(@f,[tstart tfinal],y0,options); 
   nt = length(t); 
   tout = [tout; t(2:nt)]; 
   yout = [yout; y(2:nt,:)]; 
   teout = [teout; te];           
   yeout = [yeout; ye]; 
   ieout = [ieout; ie]; 
disp(yeout) 
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); -10]; 
% -------------------------------------------------------------- 
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);    
isterminal = 1;   
direction = -1;   

The example models a bouncing ball with exactly one bounce and the ball touches the ground at t=4. The event function is configured to terminate the integration when height=0 which occurs at t=4. The tspan(end) is also set to 4.

The output from the code is:

By putting a breakpoint in the code after calling “ode23” we can check that the variables “te”, “ye” and “ie” are empty.

I hope this helps!