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BesselJ[0,x] is a smooth quasiperiodic function. NSolve is able to find all roots in the given range 0<x<50:

erg = NSolve[{BesselJ[0, x], 0 < x < 50}, x, Reals]
Show[{Plot[BesselJ[0, x], {x, 0, 50}] , Graphics[Point[{x, 0} /. erg]]}]

But if I increase the range 0<x<100 NSolve misses many of the expected 32 roots.

erg = NSolve[{BesselJ[0, x], 0 < x < 100}, x, Reals]
Show[{Plot[BesselJ[0, x], {x, 0, 100}] ,Graphics[Point[{x, 0} /. erg]]}]

Any idea why NSolve fails? Is there some kind of critical argumentsize x in the definition of BesselJ[0,x]? Thanks!

Bug introduced in 11.0 or earlier and fixed in 14.0.0 or earlier

BesselJ[0,x] is a smooth quasiperiodic function. NSolve is able to find all roots in the given range 0<x<50:

erg = NSolve[{BesselJ[0, x], 0 < x < 50}, x, Reals]
Show[{Plot[BesselJ[0, x], {x, 0, 50}] , Graphics[Point[{x, 0} /. erg]]}]

But if I increase the range 0<x<100 NSolve misses many of the expected 32 roots.

erg = NSolve[{BesselJ[0, x], 0 < x < 100}, x, Reals]
Show[{Plot[BesselJ[0, x], {x, 0, 100}] ,Graphics[Point[{x, 0} /. erg]]}]

Any idea why NSolve fails? Is there some kind of critical argumentsize x in the definition of BesselJ[0,x]? Thanks!

Plotting BesselJ[0,x]

Plot[BesselJ[0, x], {x, 54, 63},GridLines -> {BesselJZero[0, { 18, 19, 20}] // N , None}]

shows three roots, calculated by BesselJZero

Confirmation of the roots could be realized using FindRoot or NSolve.

FindRoot works well

FindRoot[BesselJ[0, x], {x, 55}](*{x\[Rule]55.7655}*)
FindRoot[BesselJ[0, x], {x, 58}] (*{x\[Rule]58.9069 }*)
FindRoot[BesselJ[0, x], {x, 61}] (*{x\[Rule]62.048}*)

but NSolve surprisingly fails

NSolve[{BesselJ[0, x  ], 55 < x < 63}, x, Reals][[1]]

and gives only one root instead of three!

Changing the intervall a little bit

NSolve[{BesselJ[0, x  ], 55 - 10 < x < 63 - 10}, x, Reals] 
(*{{x -> 46.3412}, {x -> 49.4826}, {x -> 52.6241}}*)

NSolve gives the three results as expected.

Any idea why NSolve fails in the first case? Is there some kind of critical argumentsize x in the definition of BesselJ[0,x]? Thanks!

BesselJ[0,x] is a smooth quasiperiodic function. NSolve is able to find all roots in the given range 0<x<50:

erg = NSolve[{BesselJ[0, x], 0 < x < 50}, x, Reals]
Show[{Plot[BesselJ[0, x], {x, 0, 50}] , Graphics[Point[{x, 0} /. erg]]}]

But if I increase the range 0<x<100 NSolve misses many of the expected 32 roots.

erg = NSolve[{BesselJ[0, x], 0 < x < 100}, x, Reals]
Show[{Plot[BesselJ[0, x], {x, 0, 100}] ,Graphics[Point[{x, 0} /. erg]]}]

Any idea why NSolve fails? Is there some kind of critical argumentsize x in the definition of BesselJ[0,x]? Thanks!