Issue with Differential Equation Solver

For this code:

begin

Parameters, variables, and derivatives

@parameters t x @variables T(…)
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2

MOL Discretization parameters

x_max = L
x_min = 0
nc = 20
t_min = 0 # Experiment 28
t_max = 6000 # Experiment 28

x_num = range(x_min, x_max, length = nc)
dx = (x_max - x_min) / (nc - 1)

eq = V*Dx(T(t, x)) + Dt(T(t, x)) ~ 0

bcs = [T(t_min, x) ~ Ts,
- ks * Dx(T(t, x_max)) ~ 0,
- ks * Dx(T(t, x_min)) ~ (- ϵ * σ * ((T(t, x_min)^4))) + Q - h * (T(t,x_min) - Ts) - 91.64]

Space and time domain

domains = [t ∈ Interval(t_min, t_max),
x ∈ Interval(x_min, x_max)]

Defining the PDE system

`@named pdesys = PDESystem([eq], bcs, domains, [t, x], [T(t, x)])

Solving using MOL

order = 2
discretization = MOLFiniteDifference([x => dx], t, approx_order = order)

Convert the PDE problem into an ODE problem

prob = discretize(pdesys, discretization)

Solve ODE problem

sol = solve(prob, saveat = 3)
T_exp = sol.u[T(t, x)]

md"“”

Numerical Solution

“”"
end`

I am getting this error:

`MethodError: no method matching SciMLBase.PDETimeSeriesSolution(::SciMLBase.PDETimeSeriesSolution{Float64, 1, Dict{Symbolics.Num, Matrix{Float64}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}, SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}}, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}, OrdinaryDiffEq.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.Rosenbrock5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEq.Rodas5Tableau{Float64, Float64}, SciMLBase.TimeGradientWrapper{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Vector{Float64}, Vector{Float64}}, SciMLBase.UJacobianWrapper{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Float64, Vector{Float64}}, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}, LinearSolve.InvPreconditioner{LinearAlgebra.Diagonal{Float64, Vector{Float64}}}, LinearAlgebra.Diagonal{Float64, Vector{Float64}}, Float64, Bool}, FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:forward}(), Float64}, FiniteDiff.GradientCache{Nothing, Vector{Float64}, Vector{Float64}, Float64, Val{:forward}(), Float64, Val{true}()}, Float64, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}}}, DiffEqBase.Stats, Nothing}, Nothing, Vector{Float64}, Tuple{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Vector{SymbolicUtils.BasicSymbolic{Real}}, Vector{Symbolics.Num}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}}, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}, Dict{Symbolics.Num, Interpolations.GriddedInterpolation{Float64, 2, Matrix{Float64}, Interpolations.Gridded{Interpolations.Linear{Interpolations.Throw{Interpolations.OnGrid}}}, Tuple{Vector{Float64}, Vector{Float64}}}}, DiffEqBase.Stats}, ::MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization})

Closest candidates are:

SciMLBase.PDETimeSeriesSolution(!Matched::SciMLBase.AbstractODESolution{T}, ::MethodOfLines.MOLMetadata) where T at ~/.julia/packages/MethodOfLines/uGynQ/src/interface/solution/timedep.jl:2

  1. wrap_sol(::SciMLBase.PDETimeSeriesSolution{Float64, 1, Dict{Symbolics.Num, Matrix{Float64}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}, SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}}, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}, OrdinaryDiffEq.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.Rosenbrock5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEq.Rodas5Tableau{Float64, Float64}, SciMLBase.TimeGradientWrapper{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Vector{Float64}, Vector{Float64}}, SciMLBase.UJacobianWrapper{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Float64, Vector{Float64}}, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}, LinearSolve.InvPreconditioner{LinearAlgebra.Diagonal{Float64, Vector{Float64}}}, LinearAlgebra.Diagonal{Float64, Vector{Float64}}, Float64, Bool}, FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:forward}(), Float64}, FiniteDiff.GradientCache{Nothing, Vector{Float64}, Vector{Float64}, Float64, Val{:forward}(), Float64, Val{true}()}, Float64, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}}}, DiffEqBase.Stats, Nothing}, Nothing, Vector{Float64}, Tuple{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Vector{SymbolicUtils.BasicSymbolic{Real}}, Vector{Symbolics.Num}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}}, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}, Dict{Symbolics.Num, Interpolations.GriddedInterpolation{Float64, 2, Matrix{Float64}, Interpolations.Gridded{Interpolations.Linear{Interpolations.Throw{Interpolations.OnGrid}}}, Tuple{Vector{Float64}, Vector{Float64}}}}, DiffEqBase.Stats}, ::MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization})@pde_solutions.jl:119
  2. wrap_sol(::SciMLBase.PDETimeSeriesSolution{Float64, 1, Dict{Symbolics.Num, Matrix{Float64}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}, SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}}, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}, OrdinaryDiffEq.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.Rosenbrock5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEq.Rodas5Tableau{Float64, Float64}, SciMLBase.TimeGradientWrapper{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Vector{Float64}, Vector{Float64}}, SciMLBase.UJacobianWrapper{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Float64, Vector{Float64}}, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}, LinearSolve.InvPreconditioner{LinearAlgebra.Diagonal{Float64, Vector{Float64}}}, LinearAlgebra.Diagonal{Float64, Vector{Float64}}, Float64, Bool}, FiniteDiff.JacobianCache{Vector{Float64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, UnitRange{Int64}, Nothing, Val{:forward}(), Float64}, FiniteDiff.GradientCache{Nothing, Vector{Float64}, Vector{Float64}, Float64, Val{:forward}(), Float64, Val{true}()}, Float64, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}}}, DiffEqBase.Stats, Nothing}, Nothing, Vector{Float64}, Tuple{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Vector{SymbolicUtils.BasicSymbolic{Real}}, Vector{Symbolics.Num}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}}, OrdinaryDiffEq.Rodas5P{1, false, LinearSolve.DefaultLinearSolver, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}, Dict{Symbolics.Num, Interpolations.GriddedInterpolation{Float64, 2, Matrix{Float64}, Interpolations.Gridded{Interpolations.Linear{Interpolations.Throw{Interpolations.OnGrid}}}, Tuple{Vector{Float64}, Vector{Float64}}}}, DiffEqBase.Stats})@basic_solutions.jl:98
  3. var"#solve#40"(::Nothing, ::Nothing, ::Nothing, ::Val{true}, ::Base.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:saveat,), Tuple{Int64}}}, ::typeof(CommonSolve.solve), ::SciMLBase.ODEProblem{Vector{Float64}, Tuple{Int64, Int64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.var"#k#545"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xe5c93a32, 0x2cbe7883, 0x421b7a96, 0x66e7a7df, 0xc00fbc62), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xa72d68a9, 0xa06a2668, 0xbf287d64, 0x6dfb1292, 0xdc5dd793), Nothing}}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Symbol, Vector{Any}, ModelingToolkit.var"#607#generated_observed#555"{Bool, ModelingToolkit.ODESystem, Dict{Any, Any}, Vector{Any}}, Nothing, ModelingToolkit.ODESystem}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, MethodOfLines.MOLMetadata{Val{true}(), MethodOfLines.DiscreteSpace{1, 1, MethodOfLines.CenterAlignedGrid}, MethodOfLines.MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}, ModelingToolkit.PDESystem, Base.RefValue{Any}, MethodOfLines.ScalarizedDiscretization}})@solve.jl:930
  4. top-level scope@Local: 41 [inlined]`

I have used this differential solver with for this code below and it works fine:
begin # Parameters, variables, and derivatives @parameters t x
` @variables T(…)
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2

# MOL Discretization parameters
x_max = L 
x_min = 0

t_min = 0    # Experiment 28
t_max = 6737 # 6737    # Experiment 28

nc = 20
x_num = range(x_min, x_max, length=nc)
dx = (x_max - x_min) / (nc - 1)

eq = ((52000 * exp(-1.24e-5 * T(t, x)) / (T(t, x) + 437)) / 1000) * Dxx(T(t, x)) + I0 * exp(-2300 * T(t, x)) ~ ρs * Cps * Dt(T(t, x))

bcs = [T(t_min, x) ~ Ts,
    - ((52000 * exp(-1.24e-5 * T(t, x)) / (T(t, x) + 437)) / 1000) * Dx(T(t, 	x_max)) ~ 0,
    -((52000 * exp(-1.24e-5 * T(t, x)) / (T(t, x) + 437)) / 1000) * Dx(T(t, x_min)) ~ (-(ϵ * σ * ((T(t, x_min)^4) - (Ts)^4)) + Q)]

# Space and time domain
domains = [t ∈ Interval(t_min, t_max),
    x ∈ Interval(x_min, x_max)]

# Defining the PDE system
@named pdesys = PDESystem([eq], bcs, domains, [t, x], [T(t, x)])

# Solving using MOL
order = 2
discretization = MOLFiniteDifference([x => dx], t, approx_order=order)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys, discretization)
# Solve ODE problem
sol = solve(prob, saveat=3)
T_exp = sol.u[T(t, x)]

md"""
## Numerical Solution
"""

end`

I am unsure of how to address this error, would appreciate some help!

What versions? Share ]st

The Julia version is 1.8

That’s not the full list of package versions.

Status ~/.julia/environments/v1.8/Project.toml

⌃ [093aae92] BSplineKit v0.4.0

⌃ [336ed68f] CSV v0.10.9

⌃ [35d6a980] ColorSchemes v3.20.0

[2e2c70e5] DataFitting v0.1.0

⌃ [a93c6f00] DataFrames v1.3.6

⌃ [0c46a032] DifferentialEquations v6.18.0

[607db5a9] DifferentialEvolutionMCMC v0.7.6

⌅ [5b8099bc] DomainSets v0.5.15

⌃ [f6369f11] ForwardDiff v0.10.35

⌃ [34004b35] HypergeometricFunctions v0.3.15

⌃ [4345ca2d] Loess v0.5.4

⌅ [2fda8390] LsqFit v0.11.0

⌃ [961ee093] ModelingToolkit v8.1.0

[76087f3c] NLopt v1.0.0

⌅ [8913a72c] NonlinearSolve v0.3.22

⌃ [429524aa] Optim v1.7.4

⌃ [7f7a1694] Optimization v3.11.2

⌃ [36348300] OptimizationOptimJL v0.1.5

⌅ [1dea7af3] OrdinaryDiffEq v5.55.1

[58dd65bb] Plotly v0.4.1

⌃ [91a5bcdd] Plots v1.38.7

⌃ [c3e4b0f8] Pluto v0.19.9

⌃ [7f904dfe] PlutoUI v0.7.50

⌃ [f3b207a7] StatsPlots v0.15.1

⌃ [24249f21] SymPy v1.1.12

⌃ [fdbf4ff8] XLSX v0.9.0

[b77e0a4c] InteractiveUtils

[10745b16] Statistics

Info Packages marked with ⌃ and ⌅ have new versions available, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use status --outdated

If you run ]st in the terminal it should print out the versions of the packages.

1 Like

You seem to be running fairly old versions of packages, perhaps run status --outdated and try to work that out.

This package isn’t managing its dependencies well and is keeping everything else outdated. It’s keeping everything back to before PDEs even existed in SciML. I would recommend deleting it.

1 Like

If I updated and deleted the DifferentialEvolutionMCMC v0.7.6 package and the code still does not work, any other suggestions?

Well this doesn’t even exist. Did you try removing that?

Yes, I have removed it. It seems that the differential solver is not working, I updated the package and I am facing the same error.

What does ]st show now that you have updated everything?

Status ~/.julia/environments/v1.8/Project.toml

⌃ [093aae92] BSplineKit v0.4.0

⌃ [336ed68f] CSV v0.10.9

⌃ [35d6a980] ColorSchemes v3.20.0

⌃ [a93c6f00] DataFrames v1.3.6

⌃ [0c46a032] DifferentialEquations v6.18.0

⌅ [5b8099bc] DomainSets v0.5.15

⌃ [f6369f11] ForwardDiff v0.10.35

⌃ [34004b35] HypergeometricFunctions v0.3.15

⌃ [4345ca2d] Loess v0.5.4

⌃ [2fda8390] LsqFit v0.11.0

⌃ [961ee093] ModelingToolkit v8.1.0

[76087f3c] NLopt v1.0.0

⌅ [8913a72c] NonlinearSolve v0.3.22

[429524aa] Optim v1.7.8

⌃ [7f7a1694] Optimization v3.11.2

⌃ [36348300] OptimizationOptimJL v0.1.5

⌅ [1dea7af3] OrdinaryDiffEq v5.55.1

[58dd65bb] Plotly v0.4.1

[91a5bcdd] Plots v1.39.0

⌃ [c3e4b0f8] Pluto v0.19.9

⌃ [7f904dfe] PlutoUI v0.7.50

⌃ [f3b207a7] StatsPlots v0.15.1

⌃ [24249f21] SymPy v1.1.12

⌃ [fdbf4ff8] XLSX v0.9.0

[b77e0a4c] InteractiveUtils

[10745b16] Statistics

Did you call ]up after removing the other package? The ^s indicate that you have a lot of package that are not on the latest version. OrdinaryDiffEq is currently on 6.58, so 5.55 is quite outdated.

after the update:

Status ~/.julia/environments/v1.8/Project.toml
[093aae92] BSplineKit v0.16.5
[336ed68f] CSV v0.10.11
[35d6a980] ColorSchemes v3.24.0
[a93c6f00] DataFrames v1.6.1
⌃ [0c46a032] DifferentialEquations v7.10.0
⌅ [5b8099bc] DomainSets v0.6.7
[f6369f11] ForwardDiff v0.10.36
[34004b35] HypergeometricFunctions v0.3.23
[4345ca2d] Loess v0.6.3
[2fda8390] LsqFit v0.15.0
⌃ [961ee093] ModelingToolkit v8.70.0
[76087f3c] NLopt v1.0.0
⌅ [8913a72c] NonlinearSolve v1.10.1
[429524aa] Optim v1.7.8
[7f7a1694] Optimization v3.19.1
[36348300] OptimizationOptimJL v0.1.12
[1dea7af3] OrdinaryDiffEq v6.58.0
[58dd65bb] Plotly v0.4.1
[91a5bcdd] Plots v1.39.0
⌃ [c3e4b0f8] Pluto v0.19.9
[7f904dfe] PlutoUI v0.7.52
[f3b207a7] StatsPlots v0.15.6
[24249f21] SymPy v1.1.14
[fdbf4ff8] XLSX v0.10.0
[b77e0a4c] InteractiveUtils
[10745b16] Statistics
Info Packages marked with ⌃ and ⌅ have new versions available, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use status --outdated

The solver is still not working. Do you think it has anything to do with how I wrote the PDE? since I have used the same package for a different equation and it worked (check my initial post).

Do ]add ModelingToolkit@8.72 what does it say?

You’re still having things hold you back.

this is what I get:

Updating registry at ~/.julia/registries/General.toml
Resolving package versions…
ERROR: Unsatisfiable requirements detected for package DifferentialEquations [0c46a032]:
DifferentialEquations [0c46a032] log:
├─possible versions are: 5.0.0-7.11.0 or uninstalled
├─restricted to versions * by an explicit requirement, leaving only versions 5.0.0-7.11.0
├─restricted by compatibility requirements with OrdinaryDiffEq [1dea7af3] to versions: 6.21.0-7.11.0 or uninstalled, leaving only versions: 6.21.0-7.11.0
│ └─OrdinaryDiffEq [1dea7af3] log:
│ ├─possible versions are: 4.0.0-6.58.0 or uninstalled
│ ├─restricted to versions * by an explicit requirement, leaving only versions 4.0.0-6.58.0
│ ├─restricted by compatibility requirements with ModelingToolkit [961ee093] to versions: 6.0.0-6.58.0
│ │ └─ModelingToolkit [961ee093] log:
│ │ ├─possible versions are: 0.0.1-8.72.2 or uninstalled
│ │ └─restricted to versions 8.72 by an explicit requirement, leaving only versions 8.72.0-8.72.2
│ ├─restricted by compatibility requirements with ArrayInterface [4fba245c] to versions: [4.0.0-5.13.0, 6.11.0-6.58.0] or uninstalled, leaving only versions: 6.11.0-6.58.0
│ │ └─ArrayInterface [4fba245c] log:
│ │ ├─possible versions are: 0.0.1-7.4.11 or uninstalled
│ │ ├─restricted by compatibility requirements with ModelingToolkit [961ee093] to versions: 6.0.0-7.4.11
│ │ │ └─ModelingToolkit [961ee093] log: see above
│ │ ├─restricted by compatibility requirements with VectorizationBase [3d5dd08c] to versions: 6.0.1-7.4.11
│ │ │ └─VectorizationBase [3d5dd08c] log:
│ │ │ ├─possible versions are: 0.1.0-0.21.64 or uninstalled
│ │ │ ├─restricted by julia compatibility requirements to versions: 0.20.8-0.21.64 or uninstalled
│ │ │ ├─restricted by compatibility requirements with LoopVectorization [bdcacae8] to versions: [0.19.8-0.19.39, 0.20.1-0.21.64], leaving only versions: 0.20.8-0.21.64
│ │ │ │ └─LoopVectorization [bdcacae8] log:
│ │ │ │ ├─possible versions are: 0.1.0-0.12.165 or uninstalled
│ │ │ │ ├─restricted by julia compatibility requirements to versions: 0.9.0-0.12.165 or uninstalled
│ │ │ │ ├─restricted by compatibility requirements with OrdinaryDiffEq [1dea7af3] to versions: 0.12.0-0.12.165
│ │ │ │ │ └─OrdinaryDiffEq [1dea7af3] log: see above
│ │ │ │ ├─restricted by compatibility requirements with ArrayInterface [4fba245c] to versions: [0.1.0-0.8.26, 0.12.111-0.12.165] or uninstalled, leaving only versions: 0.12.111-0.12.165
│ │ │ │ │ └─ArrayInterface [4fba245c] log: see above
│ │ │ │ └─restricted by compatibility requirements with DocStringExtensions [ffbed154] to versions: [0.1.0-0.6.30, 0.12.114-0.12.165] or uninstalled, leaving only versions: 0.12.114-0.12.165
│ │ │ │ └─DocStringExtensions [ffbed154] log:
│ │ │ │ ├─possible versions are: 0.4.6-0.9.3 or uninstalled
│ │ │ │ ├─restricted by compatibility requirements with ModelingToolkit [961ee093] to versions: 0.7.0-0.9.3
│ │ │ │ │ └─ModelingToolkit [961ee093] log: see above
│ │ │ │ ├─restricted by compatibility requirements with Optimization [7f7a1694] to versions: 0.8.0-0.9.3
│ │ │ │ │ └─Optimization [7f7a1694] log:
│ │ │ │ │ ├─possible versions are: 3.5.0-3.19.1 or uninstalled
│ │ │ │ │ ├─restricted to versions * by an explicit requirement, leaving only versions 3.5.0-3.19.1
│ │ │ │ │ ├─restricted by compatibility requirements with ModelingToolkit [961ee093] to versions: [3.5.0-3.9.2, 3.9.4-3.19.1] or uninstalled, leaving only versions: [3.5.0-3.9.2, 3.9.4-3.19.1]
│ │ │ │ │ │ └─ModelingToolkit [961ee093] log: see above
│ │ │ │ │ └─restricted by compatibility requirements with SciMLBase [0bca4576] to versions: 3.19.0-3.19.1 or uninstalled, leaving only versions: 3.19.0-3.19.1
│ │ │ │ │ └─SciMLBase [0bca4576] log:
│ │ │ │ │ ├─possible versions are: 1.0.0-2.4.1 or uninstalled
│ │ │ │ │ └─restricted by compatibility requirements with ModelingToolkit [961ee093] to versions: 2.0.1-2.4.1
│ │ │ │ │ └─ModelingToolkit [961ee093] log: see above
│ │ │ │ ├─restricted by compatibility requirements with JumpProcesses [ccbc3e58] to versions: 0.8.6-0.9.3
│ │ │ │ │ └─JumpProcesses [ccbc3e58] log:
│ │ │ │ │ ├─possible versions are: 9.0.0-9.8.0 or uninstalled
│ │ │ │ │ ├─restricted by compatibility requirements with ModelingToolkit [961ee093] to versions: 9.1.0-9.8.0
│ │ │ │ │ │ └─ModelingToolkit [961ee093] log: see above
│ │ │ │ │ └─restricted by compatibility requirements with SciMLBase [0bca4576] to versions: 9.8.0 or uninstalled, leaving only versions: 9.8.0
│ │ │ │ │ └─SciMLBase [0bca4576] log: see above
│ │ │ │ └─restricted by compatibility requirements with SymbolicIndexingInterface [2efcf032] to versions: 0.9.0-0.9.3
│ │ │ │ └─SymbolicIndexingInterface [2efcf032] log:
│ │ │ │ ├─possible versions are: 0.1.0-0.2.2 or uninstalled
│ │ │ │ └─restricted by compatibility requirements with SciMLBase [0bca4576] to versions: 0.2.0-0.2.2
│ │ │ │ └─SciMLBase [0bca4576] log: see above
│ │ │ └─restricted by compatibility requirements with ArrayInterface [4fba245c] to versions: [0.1.0-0.12.33, 0.21.34-0.21.64] or uninstalled, leaving only versions: 0.21.34-0.21.64
│ │ │ └─ArrayInterface [4fba245c] log: see above
│ │ ├─restricted by compatibility requirements with DiffEqBase [2b5f629d] to versions: 7.0.0-7.4.11
│ │ │ └─DiffEqBase [2b5f629d] log:
│ │ │ ├─possible versions are: 3.13.2-6.133.1 or uninstalled
│ │ │ ├─restricted by compatibility requirements with ModelingToolkit [961ee093] to versions: 6.103.0-6.133.1
│ │ │ │ └─ModelingToolkit [961ee093] log: see above
│ │ │ └─restricted by compatibility requirements with SciMLBase [0bca4576] to versions: [3.13.2-6.53.6, 6.130.1-6.133.1] or uninstalled, leaving only versions: 6.130.1-6.133.1
│ │ │ └─SciMLBase [0bca4576] log: see above
│ │ └─restricted by compatibility requirements with LinearSolve [7ed4a6bd] to versions: 7.4.11
│ │ └─LinearSolve [7ed4a6bd] log:
│ │ ├─possible versions are: 0.1.0-2.11.0 or uninstalled
│ │ ├─restricted by compatibility requirements with OrdinaryDiffEq [1dea7af3] to versions: [1.0.0-1.42.0, 2.1.10-2.11.0]
│ │ │ └─OrdinaryDiffEq [1dea7af3] log: see above
│ │ ├─restricted by compatibility requirements with ArrayInterface [4fba245c] to versions: 1.17.0-2.11.0 or uninstalled, leaving only versions: [1.17.0-1.42.0, 2.1.10-2.11.0]
│ │ │ └─ArrayInterface [4fba245c] log: see above
│ │ ├─restricted by compatibility requirements with DifferentialEquations [0c46a032] to versions: [1.0.0-1.42.0, 2.1.12-2.11.0], leaving only versions: [1.17.0-1.42.0, 2.1.12-2.11.0]
│ │ │ └─DifferentialEquations [0c46a032] log: see above
│ │ ├─restricted by compatibility requirements with DocStringExtensions [ffbed154] to versions: [0.1.0-0.1.6, 1.20.0-2.11.0] or uninstalled, leaving only versions: [1.20.0-1.42.0, 2.1.12-2.11.0]
│ │ │ └─DocStringExtensions [ffbed154] log: see above
│ │ └─restricted by compatibility requirements with SciMLBase [0bca4576] to versions: 2.7.0-2.11.0 or uninstalled, leaving only versions: 2.7.0-2.11.0
│ │ └─SciMLBase [0bca4576] log: see above
│ ├─restricted by compatibility requirements with DocStringExtensions [ffbed154] to versions: [4.0.0-5.52.2, 6.13.1-6.58.0] or uninstalled, leaving only versions: 6.13.1-6.58.0
│ │ └─DocStringExtensions [ffbed154] log: see above
│ └─restricted by compatibility requirements with SciMLBase [0bca4576] to versions: [4.0.0-6.6.6, 6.56.0-6.58.0] or uninstalled, leaving only versions: 6.56.0-6.58.0
│ └─SciMLBase [0bca4576] log: see above
├─restricted by compatibility requirements with BoundaryValueDiffEq [764a87c0] to versions: 5.0.0-7.10.0 or uninstalled, leaving only versions: 6.21.0-7.10.0
│ └─BoundaryValueDiffEq [764a87c0] log:
│ ├─possible versions are: 2.0.0-5.1.0 or uninstalled
│ ├─restricted by julia compatibility requirements to versions: 2.0.0-4.0.1 or uninstalled, leaving only versions: 2.0.0-4.0.1
│ ├─restricted by compatibility requirements with Reexport [189a3867] to versions: 2.6.0-5.1.0 or uninstalled, leaving only versions: 2.6.0-4.0.1
│ │ └─Reexport [189a3867] log:
│ │ ├─possible versions are: 0.2.0-1.2.2 or uninstalled
│ │ └─restricted by compatibility requirements with OptimizationOptimJL [36348300] to versions: 1.2.0-1.2.2
│ │ └─OptimizationOptimJL [36348300] log:
│ │ ├─possible versions are: 0.1.1-0.1.12 or uninstalled
│ │ └─restricted to versions * by an explicit requirement, leaving only versions 0.1.1-0.1.12
│ └─restricted by compatibility requirements with SciMLBase [0bca4576] to versions: [2.0.0-2.8.0, 5.0.0-5.1.0] or uninstalled, leaving only versions: 2.6.0-2.8.0
│ └─SciMLBase [0bca4576] log: see above
├─restricted by compatibility requirements with SciMLBase [0bca4576] to versions: [5.0.0-7.2.0, 7.10.0-7.11.0] or uninstalled, leaving only versions: [6.21.0-7.2.0, 7.10.0]
│ └─SciMLBase [0bca4576] log: see above
├─restricted by compatibility requirements with LinearSolve [7ed4a6bd] to versions: [5.0.0-6.20.0, 7.8.0-7.11.0] or uninstalled, leaving only versions: 7.10.0
│ └─LinearSolve [7ed4a6bd] log: see above
└─restricted by compatibility requirements with BoundaryValueDiffEq [764a87c0] to versions: 5.0.0-7.4.0 or uninstalled — no versions left
└─BoundaryValueDiffEq [764a87c0] log: see above

Can you start by removing your other junk and simplifying?

you mean packages that are not in use?