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Bug introduced in 11.1.0 and persisting through 11.1.1
In V11.1,
NSolve[BesselJ[0, x] == 0 && 0 < x < 20, x]
returns no solutions:
But in V11.0 (and earlier), it returns all solutions:
Is there anyway to get NSolve to solve this equation in V11.1?
(Interestingly, Solve[BesselJ[0, x] == 0 && 0 < x < 20, x] works in both, but I was particularly interested NSolve, since I was wanting to compare it with other numerical methods.)
It is a bug in V11.1. As a workaround, you can put the following in your init.m file.
Reduce`RealTNRoots;
nonElementaryQ[f_] := Module[{x}, !ListQ[Simplify`FunctionSingularities[f[x], x, "ELEM"]]]
System`TRootsDump`NIntervalRoots[f_?nonElementaryQ, ii_, prec_] := $Failed
This will disable the offending code for non-elementary functions.
In[4]:= NSolve[BesselJ[0, x] == 0 && 0 < x < 20, x]
Out[4]= {{x -> 2.40483}, {x -> 5.52008}, {x -> 8.65373}, {x -> 11.7915},
> {x -> 14.9309}, {x -> 18.0711}}
Is there anyway to get NSolve to solve this equation in V11.1?
Adding Complexes makes it work
NSolve[BesselJ[0, x] == 0 && 0 < x < 20, x, Complexes]
NSolve[BesselJ[0, x] == 0 && 0 < Re[x] < 20, x] and NSolve[BesselJ[0, x] == 0 && 0 < Re[x] < 20 && Im[x] == 0, x] also work (suggested by your answer). I don't understand the reason for the change, since it breaks previous code.
$\endgroup$
– Michael E2
Apr 18 '17 at 11:58
NSolve[Zeta[x] - 2 == 0 && 0 < Re@x < 2 && Im[x] == 0, x] takes 4.5 sec and NSolve[Zeta[x] - 2 == 0 && 1 < x < 2, x, Complexes] takes 18.5 sec.; NSolve[-2 + Zeta[x] == 0 && 1 < Re[x] < 2, x] fails (but that's not surprising -- I was more surprised it worked on the Bessel funciton).
$\endgroup$
– Michael E2
Apr 18 '17 at 13:28
NSolve[]works fine. $\endgroup$ – J. M.'s ennui♦ Apr 18 '17 at 13:54NSolve[BesselJ[0, x] == 0 && 0 < x < 20, x, Abracadabra] // Quiet:) $\endgroup$ – Mariusz Iwaniuk Apr 24 '17 at 11:14