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differential equations - Spurious Error Messages from NDSolve when Using WhenEvent with Time Delays


Bug introduced between versions 10.1 and 10.4, and resolved in 11.3.


Using either 11.2 or 10.4 on Windows 10 (64 bit), I am unable to reproduce the answer by March to question 99576. Specifically,


timeLimit = 10; 
z[t_] = Piecewise[{{1, t <= 2}, {3/2, 2 < t <= 5}}, 2]; 
NDSolve[{x'[t] == 1/1.5 t, WhenEvent[x[t] == z[t], a[t] -> t], 
    WhenEvent[t == a[t] + 1, {x[t] -> 0, a[t] -> 0}], 
    a[t /; t <= 0] == timeLimit, x[t /; t <= 0] == 0}, 
    {x[t], a[t]}, {t, 0, timeLimit}, DiscreteVariables -> {a}];



NDSolve::overdet: There are fewer dependent variables, {x[t],a[t]}, than equations, so the system is overdetermined. >>



Is this a bug? Is there a work-around?


Work-Around


Szabolcs provides a work-around in a comment below, "change a[t /; t <= 0] to a[0] and the same for x". It also works for the problem I originally set out to solve, a delay differential equation, but only because my initial conditions for t <= 0 are constant. Even then, Mathematica 11.2 returns the warning message



NDSolve::ihist : Conditions given at t = 0 will be interpreted as initial history functions for t /; t <= 0.



before returning the correct answer.



Addendum: "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)" gives the correct answer without error or warning messages.




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