MWE showing DifferentialEquations.jl inputting out of domain values

mwe.jl

using OrdinaryDiffEq
const R = 8.31446261815324

function EDO(u, t)
    @info "Got:" u, t

    # Se eu usar isto, o solver passa Inf como o próximo u.
    # u = min(max(u, 0.0), 1.0) # Saturator

    A = 2.23362e12
    m = -1.922
    q = 1.0296
    n = 0.358357

    return A * exp(-1.26499e5 / (R * t)) * u^m * (1 - q * u)^n;
end

solver = AutoTsit5(Rosenbrock23())
∂α_∂t(u, _, t) = EDO(u, t)
tspan = (120.0, 184.0)
u₀ = 1e-8
prob = ODEProblem(∂α_∂t, u₀, tspan)
solution = solve(prob, solver)
#=
┌ Info: Data:
└   (u, t) = (7.236826308994673e-9, 182.94357305006358)
┌ Info: Data:
└   (u, t) = (-3.4088088050304658e-9, 184.0)
ERROR: LoadError: DomainError with -0.02960000000000007:
Exponentiation yielding a complex result requires a complex argument.
Replace x^y with (x+0im)^y, Complex(x)^y, or similar.
Stacktrace:
  [1] throw_exp_domainerror(x::Float64)
    @ Base.Math ./math.jl:37
  [2] ^
    @ ./math.jl:909 [inlined]
  [3] EDO(u::Float64, t::Float64)
    @ Main ~/Documents/mwe.jl:14
  [4] ∂α_∂t
    @ ~/Documents/mwe.jl:18 [inlined]
  [5] ODEFunction
    @ ~/.julia/packages/SciMLBase/h4Gxc/src/scimlfunctions.jl:334 [inlined]
  [6] perform_step!(integrator::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}, false, Float64, Nothing, Float64, SciMLBase.NullParameters, Float64, Float64, Float64, Float64, Vector{Float64}, OrdinaryDiffEq.ODECompositeSolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Float64}}, ODEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, CompositeAlgorithm{Tuple{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}, OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Float64}, Vector{Float64}, Vector{Vector{Float64}}, OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}, OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64, SciMLBase.TimeDerivativeWrapper{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, SciMLBase.NullParameters}, SciMLBase.UDerivativeWrapper{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, SciMLBase.NullParameters}, Float64, Float64, DefaultLinSolve}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}}, DiffEqBase.DEStats}, ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}, OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64, SciMLBase.TimeDerivativeWrapper{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, SciMLBase.NullParameters}, SciMLBase.UDerivativeWrapper{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, SciMLBase.NullParameters}, Float64, Float64, DefaultLinSolve}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Nothing, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Float64, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, cache::OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}, repeat_step::Bool)
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/Zi9Zh/src/perform_step/low_order_rk_perform_step.jl:589
  [7] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEq/Zi9Zh/src/perform_step/composite_perform_step.jl:50 [inlined]
  [8] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEq/Zi9Zh/src/perform_step/composite_perform_step.jl:49 [inlined]
  [9] solve!(integrator::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}, false, Float64, Nothing, Float64, SciMLBase.NullParameters, Float64, Float64, Float64, Float64, Vector{Float64}, OrdinaryDiffEq.ODECompositeSolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Float64}}, ODEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, CompositeAlgorithm{Tuple{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}, OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Float64}, Vector{Float64}, Vector{Vector{Float64}}, OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}, OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64, SciMLBase.TimeDerivativeWrapper{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, SciMLBase.NullParameters}, SciMLBase.UDerivativeWrapper{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, SciMLBase.NullParameters}, Float64, Float64, DefaultLinSolve}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}}, DiffEqBase.DEStats}, ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}, OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64, SciMLBase.TimeDerivativeWrapper{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, SciMLBase.NullParameters}, SciMLBase.UDerivativeWrapper{ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Float64, SciMLBase.NullParameters}, Float64, Float64, DefaultLinSolve}}, OrdinaryDiffEq.AutoSwitchCache{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Nothing, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Float64, Float64, Nothing, OrdinaryDiffEq.DefaultInit})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/Zi9Zh/src/solve.jl:478
 [10] #__solve#475
    @ ~/.julia/packages/OrdinaryDiffEq/Zi9Zh/src/solve.jl:5 [inlined]
 [11] __solve
    @ ~/.julia/packages/OrdinaryDiffEq/Zi9Zh/src/solve.jl:4 [inlined]
 [12] #solve_call#42
    @ ~/.julia/packages/DiffEqBase/Samo4/src/solve.jl:61 [inlined]
 [13] solve_call(_prob::ODEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, args::CompositeAlgorithm{Tuple{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}}, AutoSwitch{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Samo4/src/solve.jl:48
 [14] solve_up(prob::ODEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, sensealg::Nothing, u0::Float64, p::SciMLBase.NullParameters, args::CompositeAlgorithm{Tuple{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}}, AutoSwitch{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}}; kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Samo4/src/solve.jl:87
 [15] solve_up
    @ ~/.julia/packages/DiffEqBase/Samo4/src/solve.jl:78 [inlined]
 [16] #solve#43
    @ ~/.julia/packages/DiffEqBase/Samo4/src/solve.jl:73 [inlined]
 [17] solve(prob::ODEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, ODEFunction{false, typeof(∂α_∂t), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, args::CompositeAlgorithm{Tuple{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}}, AutoSwitch{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, Rosenbrock23{0, true, DefaultLinSolve, Val{:forward}}, Rational{Int64}, Int64}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Samo4/src/solve.jl:68
 [18] top-level scope
    @ ~/Documents/mwe.jl:22
in expression starting at /home/helitonmrf/Documents/mwe.jl:22
=#