Why does this ODE yield two events?

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Darren Wethington 2019-3-4

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编辑： Darren Wethington 2019-3-7

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I have the following simple ODE:

With initial condition x(0)=5, I am interested in when x(t)==1. So I have the following events function:

function [value,isterminal,direction] = test_events(t,x)
value = x-1;
isterminal = 0;
direction = 0;
end

This should produce an event at t=4. However, if I run the following code I get two events, one at t=4, and one at t=4+5.7e-14:

options = odeset('Events',@test_events);
sol = ode45(@(t,x)-1,[0 10],5,options);

If I run smiliar codes to find when x(t)==0 or x(t)==-1 (value = x; or value = x+1; respectively), I have only one event. Why does this generate two events?

NEWER UPDATE:

Observing the sol.x and sol.y outputs (t and x, respectively), the time progresses as integers [0 1 2 3 4 5 6 7...], and x progresses as integers up until x(t=5) like so: [5 4 3 2 1 1.11e-16 -1.000 -2.000...]. This indicates that there is something that occurs between t=4 and t=5 that creates a 'bump' in the ODE solution. Why?

OLDER UPDATE:

If the relative tolerance is set to 1e-5, the solver provides a single event correctly at t=4. If the relative tolerance is set to 1e-4, the solver provides a single event, but at t=4+5.7e-14. If the relative tolerance is set to 1e-8, the solver produces the same two events as the default. If the initial condition is changed from x(0)=5 to x(0)=4, the solver yields one event. However, if the initial condition is changed to x(0)=4 and the RelTol is set to 1e-8, it generates two events.