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I'm solving an ODE system with multiple events and find the discrete variable not updated as expected because one of the events is not triggered. During narrowing down the problem, I find something strange and cannot explain. Here are the simplified cases.

Case 1 works perfectly in the sense that the two events occur as expected. Case 2 does not work. Case 3 works by removing the action a[t] -> t in case 2 although the discrete variable won't get updated any longer.

Case 1

NDSolveValue[{y'[t] == Cos[t], y[0] == a[0] == 0, 
  WhenEvent[y[t], {Print[1], a[t] -> t}], 
  WhenEvent[t == a[t] + 0.1, Print[3]]}, y, {t, 0, 20}, DiscreteVariables -> a]

Case 2

NDSolveValue[{y'[t] == Cos[t], y[0] == a[0] == 0, 
  WhenEvent[y'[t], {Print[1], a[t] -> t}], 
  WhenEvent[t == a[t] + 0.1, Print[3]]}, y, {t, 0, 20}, DiscreteVariables -> a]

Case 3

NDSolveValue[{y'[t] == Cos[t], y[0] == a[0] == 0, 
  WhenEvent[y'[t], Print[1]], 
  WhenEvent[t == a[t] + 0.1, Print[3]]}, y, {t, 0, 20}, DiscreteVariables -> a]

Maybe this issue is not relevant to the real case. But how to understand the action a[t] -> t will stop the event from happening while it is not even part of the ODE? And why is only y' affected in this case?

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  • 1
    $\begingroup$ In case 2, I get that the integration stops at the starting value t == 0. The events never happen. So, to me, the first question to investigate is why NDSolve[] quits right away. $\endgroup$ Commented Oct 21 at 18:04
  • 3
    $\begingroup$ A tentative answer is that Null, the value returned by Print[1], is not really a valid action. Sometimes it causes trouble, sometimes it doesn't (~ GIGO). If the action is {Print[1]; a[t] -> t}, then it seems to work. $\endgroup$ Commented Oct 21 at 18:30

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