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?