# Problem with NDSolveValue : "The function value {$Failed} is not a list of numbers with \ dimensions..." I was having fun modifying a code given to me as an answer to a previous problem here, courtesy of user Alex Trounev (Thank you again), when I encountered a certain error which I had never seen before. Here is the aforesaid code : (*parameters*) r0 = 0.5; h = 1; α = 0.8; (*region definition*) reg = Cuboid[{.5, 0., 0.}, {1., 2 Pi, 1.}]; reg3D = ImplicitRegion[ r0^2 <= x^2 + y^2 <= 1 && 0 <= z <= 1, {x, y, z}]; (*equation + conditions*) eq1 = D[u[t, r, θ, z], t] - (D[u[t, r, θ, z], r, r] + 1/r*D[u[t, r, θ, z], r] - 1/(α^2 r^2) D[u[t, r, θ, z], θ, θ] + D[u[t, r, θ, z], z, z]); ic = u[0, r, θ, z] == 1; bc = DirichletCondition[u[t, r, θ, z] == Exp[-5 t], r == r0]; nV = NeumannValue[1, r == 1]; pbc = PeriodicBoundaryCondition[u[t, r, θ, z], θ == 0, TranslationTransform[{0, 2 π*α, 0}]]; (*solution computation*) sol = NDSolveValue[{eq1 == nV, ic, bc, pbc}, u, {t, 0, 2}, {r, θ, z} ∈ reg]; (*frames=Table[DensityPlot3D[sol[t,Sqrt[x^2+y^2],ArcTan[x,y],z],{x,y,\ z}∈reg3D,ColorFunction\[Rule]"Rainbow",OpacityFunction\[Rule]\ None,Boxed\[Rule]False,Axes\[Rule]False,PlotRange\[Rule]{0,1.5},\ PlotPoints\[Rule]50,PlotLabel\[Rule]Row[{"t = \ ",t}],ColorFunctionScaling\[Rule]False],{t,.05,1,.05}] ListAnimate[frames]*) When I run the code, after some time, I get greeted with the following error : NDSolveValue::nlnum: The function value {$Failed} is not a list of numbers with dimensions {39639} at {t,u[t,r,θ,z],(u^(1,0,0,0))[t,r,θ,z]} = {0.0138161,{<<1>>},{-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,<<15>>,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,-4.66626,<<39589>>}}.

When I click on the three dots next to the error, I don't find any information on the error like it's usually the case. I then decide to google some answers. I found some answers here while also trying to comprehend the error by looking at this and finally that answer here.

So if I did understand it correctly, such error arises when you use NDSolve (or NDSolveValue) to get a symbolical solution to your equation, but problems come up when you try to numerically evaluate it for plotting purpose, or when trying to get a symbolical result with a function that requires numerical values ?

In any case, I do not really understand why I get such error as my plot part is currently between (* ... *) so it shouldn't matter. As for the rest of the code, I do not really see an error but I am just a beginner so...

Anyway, can a kind fellow enlighten me please ?

Edit 1 : Yes I forgot to tell you that this is quite the time-consuming computation...sorry.

• I got tired of waiting for it to finish....sorry. Jul 5, 2020 at 1:57
• @MichaelE2 I reproduced the error after nearly an hour on my six-processor computer. The computation consumed nearly every available cycle. It produce an InterpolatingFunction over {t, 0, 0.0138}, which appears to go unstable by t = 5 10^-4 Jul 5, 2020 at 4:03
• There appears to be a sign error in eq1. - 1/(\[Alpha]^2 r^2) D[u[t, r, \[Theta], z], \[Theta], \[Theta]] should be 1/(\[Alpha]^2 r^2) D[u[t, r, \[Theta], z], \[Theta], \[Theta]]. Correct it, and the computation runs correctly. Jul 5, 2020 at 4:17
• @MichaelE2 It's alright, don't bother, ty nonetheless. Jul 5, 2020 at 10:01
• @bbgodfrey Yes, changing the " - " into a "+" fixes the issue...but why does it fix the issue though ? That I'd like to understand. Jul 5, 2020 at 10:03