Chemical Akzo Nobel Differential-Algebraic Equation (DAE) Work-Precision Diagrams

using OrdinaryDiffEq, DiffEqDevTools, Sundials, ModelingToolkit, ODEInterfaceDiffEq,
      Plots, DASSL, DASKR
using OrdinaryDiffEqBDF, OrdinaryDiffEqFIRK, OrdinaryDiffEqRosenbrock, OrdinaryDiffEqSDIRK
using LinearAlgebra
using ModelingToolkit: t_nounits as t, D_nounits as D

ModelingToolkit.@parameters begin
    k₁=18.7
    k₂=0.58
    k₃=0.09
    k₄=0.42
    kbig=34.4
    kla=3.3
    ks=115.83
    po2=0.9
    hen=737
end

@variables begin
    y₁(t) = 0.444
    y₂(t) = 0.00123
    y₃(t) = 0.0
    y₄(t) = 0.007
    y₅(t) = 1.0
    y₆(t) = 115.83*0.444*0.007 # ks*y₁*y₄
end

r₁ = k₁ * (y₁^4.0) * sqrt(abs(y₂))
r₂ = k₂ * y₃ * y₄
r₃ = k₂/kbig * y₁ * y₅
r₄ = k₃*y₁*(y₄^2)
r₅ = k₄*(y₆^2)*sqrt(abs(y₂))
fin = kla*(po2/hen-y₂)

eqs = [D(y₁) ~ -2.0 * r₁ + r₂ - r₃ - r₄
       D(y₂) ~ -0.5 * r₁ - r₄ - 0.5*r₅ + fin
       D(y₃) ~ r₁ - r₂ + r₃
       D(y₄) ~ -r₂ + r₃ - 2.0 * r₄
       D(y₅) ~ r₂ - r₃ + r₅
       0.0 ~ ks * y₁ * y₄ - y₆]

# @mtkcompile drops y₆ (algebraic). Residual DAE form is hand-written so IDA
# runs on the original 6-variable index-1 system (MTK DAEProblem + IDA hits a
# KINSOL handle double-free on finalize for the reduced pure-ODE system).
ModelingToolkit.@mtkcompile sys = ModelingToolkit.System(eqs, t)

tspan = (0.0, 180.0)
mtkprob = ODEProblem(sys, [], tspan; warn_initialize_determined = false)
sol = solve(mtkprob, Rodas4(), abstol = 1 / 10^14, reltol = 1 / 10^14)

odaeprob = ODEProblem(sys, [], tspan; warn_initialize_determined = false)
ode_ref_sol = solve(odaeprob, CVODE_BDF(), abstol = 1 / 10^14, reltol = 1 / 10^14)

function akzo(du, u, p, t)
    y₁, y₂, y₃, y₄, y₅, y₆ = u
    k₁ = 18.7
    k₂ = 0.58
    k₃ = 0.09
    k₄ = 0.42
    kbig = 34.4
    kla = 3.3
    ks = 115.83
    po2 = 0.9
    hen = 737

    r₁ = k₁ * (y₁^4.0) * sqrt(abs(y₂))
    r₂ = k₂ * y₃ * y₄
    r₃ = k₂ / kbig * y₁ * y₅
    r₄ = k₃ * y₁ * (y₄^2)
    r₅ = k₄ * (y₆^2) * sqrt(abs(y₂))
    fin = kla * (po2 / hen - y₂)

    du[1] = -2.0 * r₁ + r₂ - r₃ - r₄
    du[2] = -0.5 * r₁ - r₄ - 0.5 * r₅ + fin
    du[3] = r₁ - r₂ + r₃
    du[4] = -r₂ + r₃ - 2.0 * r₄
    du[5] = r₂ - r₃ + r₅
    du[6] = ks * y₁ * y₄ - y₆
    nothing
end

function akzo_dae!(res, du, u, p, t)
    y₁, y₂, y₃, y₄, y₅, y₆ = u
    k₁ = 18.7
    k₂ = 0.58
    k₃ = 0.09
    k₄ = 0.42
    kbig = 34.4
    kla = 3.3
    ks = 115.83
    po2 = 0.9
    hen = 737

    r₁ = k₁ * (y₁^4.0) * sqrt(abs(y₂))
    r₂ = k₂ * y₃ * y₄
    r₃ = k₂ / kbig * y₁ * y₅
    r₄ = k₃ * y₁ * (y₄^2)
    r₅ = k₄ * (y₆^2) * sqrt(abs(y₂))
    fin = kla * (po2 / hen - y₂)

    res[1] = du[1] - (-2.0 * r₁ + r₂ - r₃ - r₄)
    res[2] = du[2] - (-0.5 * r₁ - r₄ - 0.5 * r₅ + fin)
    res[3] = du[3] - (r₁ - r₂ + r₃)
    res[4] = du[4] - (-r₂ + r₃ - 2.0 * r₄)
    res[5] = du[5] - (r₂ - r₃ + r₅)
    res[6] = ks * y₁ * y₄ - y₆
    nothing
end

u0_akzo = [0.444, 0.00123, 0.0, 0.007, 1.0, 115.83 * 0.444 * 0.007]
du0_akzo = zeros(6)
akzo(du0_akzo, u0_akzo, nothing, 0.0)
du0_akzo[6] = 0.0
daeprob = DAEProblem(akzo_dae!, du0_akzo, u0_akzo, tspan;
    differential_vars = [true, true, true, true, true, false])
ref_sol = solve(daeprob, IDA(), abstol = 1 / 10^14, reltol = 1 / 10^14)

M = Matrix{Float64}(I, 6, 6)
M[6, 6] = 0
mmf = ODEFunction(akzo, mass_matrix = M)
mmprob = ODEProblem(mmf, u0_akzo, tspan)
mm_refsol = solve(mmprob, Rodas5(), reltol = 1e-12, abstol = 1e-12)

# mtkprob/odaeprob are the 5-state reduced ODE; daeprob/mmprob are the
# original 6-state index-1 form. Pair each with a matching reference.
probs = [mtkprob, daeprob, odaeprob, mmprob]
refs = [ode_ref_sol, ref_sol, ode_ref_sol, mm_refsol]

4-element Vector{SciMLBase.AbstractODESolution{Float64, 2, Vector{Vector{Fl
oat64}}}}:
 [1.0 0.9999999999999939 … 2.2052359839597386 2.206487991523823; 0.00700000
0000000001 0.007000000000008238 … 0.06619887692323057 0.06618776708641433; 
… ; 0.00123 0.0012299999999848845 … 8.217320767237999e-5 8.236623734555439e
-5; 0.444 0.4439999999999356 … 0.17932450881249204 0.17923669493534578]
 [0.444 0.4439999999999922 … 0.1793257826485749 0.17923669493574396; 0.0012
3 0.0012299999999981612 … 8.217041113084348e-5 8.236623734513624e-5; … ; 1.
0 0.9999999999999992 … 2.205217828770764 2.2064879915224864; 0.35999964 0.3
599996400000452 … 1.3750404368805869 1.3741233306366074]
 [1.0 0.9999999999999939 … 2.2052359839597386 2.206487991523823; 0.00700000
0000000001 0.007000000000008238 … 0.06619887692323057 0.06618776708641433; 
… ; 0.00123 0.0012299999999848845 … 8.217320767237999e-5 8.236623734555439e
-5; 0.444 0.4439999999999356 … 0.17932450881249204 0.17923669493534578]
 [0.444 0.4439999415372921 … 0.1792368384837873 0.17923669493580427; 0.0012
3 0.0012299862707410296 … 8.236592192291408e-5 8.236623785721163e-5; … ; 1.
0 0.9999999944229508 … 2.206485944159063 2.206487991522178; 0.35999964 0.35
99999773926656 … 1.3741248082628827 1.3741233306373841]

plot(ref_sol)

plot(mm_refsol)

High Tolerances

abstols = 1.0 ./ 10.0 .^ (5:8)
reltols = 1.0 ./ 10.0 .^ (1:4);
setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()),
    Dict(:prob_choice => 1, :alg=>Rodas4()),
    Dict(:prob_choice => 1, :alg=>FBDF()),
    Dict(:prob_choice => 1, :alg=>QNDF()),
    Dict(:prob_choice => 1, :alg=>NordsieckBDF()),
    Dict(:prob_choice => 1, :alg=>rodas()),
    Dict(:prob_choice => 1, :alg=>radau()),
    Dict(:prob_choice => 1, :alg=>RadauIIA5()),
    Dict(:prob_choice => 2, :alg=>DFBDF()),
    Dict(:prob_choice => 2, :alg=>DNordsieckBDF()),
    Dict(:prob_choice => 2, :alg=>IDA())
]

wp = WorkPrecisionSet(probs, abstols, reltols, setups;
    save_everystep = false, appxsol = refs, maxiters = Int(1e5), numruns = 10)
plot(wp)

abstols = 1.0 ./ 10.0 .^ (6:8)
reltols = 1.0 ./ 10.0 .^ (2:4);
setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()),
    Dict(:prob_choice => 1, :alg=>Rodas4()),
    Dict(:prob_choice => 2, :alg=>IDA()),
    Dict(:prob_choice => 3, :alg=>Rosenbrock23()),
    Dict(:prob_choice => 3, :alg=>Rodas4()),
    Dict(:prob_choice => 3, :alg=>CVODE_BDF()),
    Dict(:prob_choice => 3, :alg=>TRBDF2()),
    Dict(:prob_choice => 3, :alg=>KenCarp4()),
    Dict(:prob_choice => 4, :alg=>Rodas4())
]
wp = WorkPrecisionSet(probs, abstols, reltols, setups;
    save_everystep = false, appxsol = refs, maxiters = Int(1e5), numruns = 10)
plot(wp)

abstols = 1.0 ./ 10.0 .^ (6:8)
reltols = 1.0 ./ 10.0 .^ (3:5);
setups = [Dict(:prob_choice => 3, :alg=>Rosenbrock23()),
    Dict(:prob_choice => 3, :alg=>Rodas4()),
    Dict(:prob_choice => 2, :alg=>IDA()),
    Dict(:prob_choice => 2, :alg=>DASSL.dassl()),
    Dict(:prob_choice => 2, :alg=>DASKR.daskr())
]
wp = WorkPrecisionSet(probs, abstols, reltols, setups;
    save_everystep = false, appxsol = refs, maxiters = Int(1e5), numruns = 10)
plot(wp)

Timeseries Errors

abstols = 1.0 ./ 10.0 .^ (5:8)
reltols = 1.0 ./ 10.0 .^ (1:4);
setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()),
    Dict(:prob_choice => 1, :alg=>Rodas4()),
    Dict(:prob_choice => 1, :alg=>FBDF()),
    Dict(:prob_choice => 1, :alg=>QNDF()),
    Dict(:prob_choice => 1, :alg=>NordsieckBDF()),
    Dict(:prob_choice => 1, :alg=>rodas()),
    Dict(:prob_choice => 1, :alg=>radau()),
    Dict(:prob_choice => 1, :alg=>RadauIIA5()),
    Dict(:prob_choice => 2, :alg=>DFBDF()),
    Dict(:prob_choice => 2, :alg=>DNordsieckBDF()),
    Dict(:prob_choice => 2, :alg=>IDA())
]
wp = WorkPrecisionSet(probs, abstols, reltols, setups; error_estimate = :l2,
    save_everystep = false, appxsol = refs, maxiters = Int(1e5), numruns = 10)
plot(wp)

abstols = 1.0 ./ 10.0 .^ (6:8)
reltols = 1.0 ./ 10.0 .^ (2:4);
setups = [Dict(:prob_choice => 1, :alg=>Rosenbrock23()),
    Dict(:prob_choice => 1, :alg=>Rodas4()),
    Dict(:prob_choice => 2, :alg=>IDA()),
    Dict(:prob_choice => 3, :alg=>Rosenbrock23()),
    Dict(:prob_choice => 3, :alg=>Rodas4()),
    Dict(:prob_choice => 3, :alg=>CVODE_BDF()),
    Dict(:prob_choice => 3, :alg=>TRBDF2()),
    Dict(:prob_choice => 3, :alg=>KenCarp4())
]
wp = WorkPrecisionSet(probs, abstols, reltols, setups; error_estimate = :l2,
    save_everystep = false, appxsol = refs, maxiters = Int(1e5), numruns = 10)
plot(wp)

Low Tolerances

This is the speed at lower tolerances, measuring what's good when accuracy is needed.

abstols = 1.0 ./ 10.0 .^ (7:12)
reltols = 1.0 ./ 10.0 .^ (4:9)

setups = [Dict(:prob_choice => 1, :alg=>Rodas5()),
    Dict(:prob_choice => 3, :alg=>Rodas5()),
    Dict(:prob_choice => 4, :alg=>Rodas5()),
    Dict(:prob_choice => 1, :alg=>Rodas4()),
    Dict(:prob_choice => 3, :alg=>Rodas4()),
    Dict(:prob_choice => 4, :alg=>Rodas4()),
    Dict(:prob_choice => 1, :alg=>FBDF()),
    Dict(:prob_choice => 1, :alg=>QNDF()),
    Dict(:prob_choice => 1, :alg=>NordsieckBDF()),
    Dict(:prob_choice => 1, :alg=>rodas()),
    Dict(:prob_choice => 1, :alg=>radau()),
    Dict(:prob_choice => 1, :alg=>RadauIIA5()),
    Dict(:prob_choice => 2, :alg=>DFBDF()),
    Dict(:prob_choice => 2, :alg=>DNordsieckBDF()),
    Dict(:prob_choice => 2, :alg=>IDA()),
    Dict(:prob_choice => 2, :alg=>DASKR.daskr())
]

wp = WorkPrecisionSet(probs, abstols, reltols, setups;
    save_everystep = false, appxsol = refs, maxiters = Int(1e5), numruns = 10)
plot(wp)

DASKR--  AT CURRENT T (=R1)  500 STEPS                                    
      
      In above message,  R1 =  0.1619205806876D+03
 DASKR--  TAKEN ON THIS CALL BEFORE REACHING TOUT                          
      
 DASKR--  AT CURRENT T (=R1)  500 STEPS                                    
      
      In above message,  R1 =  0.4458849558602D+02
 DASKR--  TAKEN ON THIS CALL BEFORE REACHING TOUT

wp = WorkPrecisionSet(probs, abstols, reltols, setups; error_estimate = :l2,
    save_everystep = false, appxsol = refs, maxiters = Int(1e5), numruns = 10)
plot(wp)

DASKR--  AT CURRENT T (=R1)  500 STEPS                                    
      
      In above message,  R1 =  0.1619205806876D+03
 DASKR--  TAKEN ON THIS CALL BEFORE REACHING TOUT                          
      
 DASKR--  AT CURRENT T (=R1)  500 STEPS                                    
      
      In above message,  R1 =  0.4458849558602D+02
 DASKR--  TAKEN ON THIS CALL BEFORE REACHING TOUT

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/DAE","ChemicalAkzoNobel.jmd")

Computer Information:

Julia Version 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver2)
Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

Package Information:

Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/DAE/Project.toml`
  [165a45c3] DASKR v3.2.0
  [e993076c] DASSL v3.2.0
  [f3b72e0c] DiffEqDevTools v3.6.3
  [961ee093] ModelingToolkit v11.43.1
⌅ [09606e27] ODEInterfaceDiffEq v4.1.0
  [1dea7af3] OrdinaryDiffEq v7.8.1
⌃ [6ad6398a] OrdinaryDiffEqBDF v2.4.9
  [5960d6e9] OrdinaryDiffEqFIRK v2.8.7
  [43230ef6] OrdinaryDiffEqRosenbrock v2.7.3
⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.4
  [91a5bcdd] Plots v1.41.7
  [31c91b34] SciMLBenchmarks v0.2.1
  [90137ffa] StaticArrays v1.9.20
  [10745b16] Statistics v1.11.5
  [c3572dad] Sundials v6.7.1
  [0c5d862f] Symbolics v7.39.2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`

And the full manifest:

Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/DAE/Manifest.toml`
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⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.4
  [b1df2697] OrdinaryDiffEqTsit5 v2.1.4
  [79d7bb75] OrdinaryDiffEqVerner v2.4.1
  [90014a1f] PDMats v0.11.41
⌅ [69de0a69] Parsers v2.8.8
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.7
  [e409e4f3] PoissonRandom v0.4.13
  [f517fe37] Polyester v0.7.19
  [1d0040c9] PolyesterWeave v0.2.2
  [d236fae5] PreallocationTools v1.7.1
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.6.0
  [08abe8d2] PrettyTables v3.4.8
  [27ebfcd6] Primes v0.5.7
  [43287f4e] PtrArrays v1.4.0
  [0c0d3e7f] PureKLU v1.5.0
  [1fd47b50] QuadGK v2.11.3
  [988b38a3] ReadOnlyArrays v0.2.0
  [795d4caa] ReadOnlyDicts v1.0.1
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v4.5.1
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.4.0
  [9fe22ead] RespecializeParams v1.3.0
  [79098fc4] Rmath v0.9.0
  [47965b36] RootedTrees v2.27.0
  [f2b01f46] Roots v3.0.8
  [7e49a35a] RuntimeGeneratedFunctions v0.5.26
  [9dfe8606] SCCNonlinearSolve v1.15.3
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v3.54.0
  [31c91b34] SciMLBenchmarks v0.2.1
  [19f34311] SciMLJacobianOperators v0.1.19
  [a6db7da4] SciMLLogging v2.1.0
⌃ [c0aeaf25] SciMLOperators v1.30.0
  [431bcebd] SciMLPublic v1.3.0
  [53ae85a6] SciMLStructures v1.10.5
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [992d4aef] Showoff v1.1.1
  [727e6d20] SimpleNonlinearSolve v2.14.5
  [699a6c99] SimpleTraits v0.9.6
  [a2af1166] SortingAlgorithms v1.2.3
  [a57abbd0] SparseColumnPivotedQR v2.1.8
  [0a514795] SparseMatrixColorings v0.4.28
  [276daf66] SpecialFunctions v2.9.0
  [860ef19b] StableRNGs v1.0.4
  [0c0c59c1] StarAlgebras v0.3.0
  [64909d44] StateSelection v1.11.1
  [aedffcd0] Static v1.4.6
  [0d7ed370] StaticArrayInterface v1.10.0
  [90137ffa] StaticArrays v1.9.20
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.5
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.13
  [4c63d2b9] StatsFuns v2.2.1
  [7792a7ef] StrideArraysCore v0.5.9
  [69024149] StringEncodings v0.3.7
⌅ [892a3eda] StringManipulation v0.5.0
  [09ab397b] StructArrays v0.7.3
  [c3572dad] Sundials v6.7.1
  [2efcf032] SymbolicIndexingInterface v0.3.55
  [19f23fe9] SymbolicLimits v1.2.1
  [d1185830] SymbolicUtils v4.46.6
  [0c5d862f] Symbolics v7.39.2
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.14.0
  [ed4db957] TaskLocalValues v0.1.3
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
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  [a759f4b9] TimerOutputs v1.2.1
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [41fe7b60] Unzip v0.2.0
  [d30d5f5c] WeakCacheSets v0.1.0
  [44d3d7a6] Weave v0.10.12
  [ddb6d928] YAML v0.4.16
  [6e34b625] Bzip2_jll v1.0.9+0
  [83423d85] Cairo_jll v1.18.7+0
  [655fdf9c] DASKR_jll v1.0.1+0
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.8.4+0
⌅ [b22a6f82] FFMPEG_jll v8.1.2+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.14.3+1
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.5.1+0
  [d2c73de3] GR_jll v0.73.27+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [7746bdde] Glib_jll v2.88.3+0
  [3b182d85] Graphite2_jll v1.3.16+0
  [2e76f6c2] HarfBuzz_jll v100.14004.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [aacddb02] JpegTurbo_jll v3.2.0+1
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.2.0+0
  [1d63c593] LLVMOpenMP_jll v23.1.1+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.42.0+0
  [89763e89] Libtiff_jll v4.7.3+0
  [38a345b3] Libuuid_jll v2.42.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [c771fb93] ODEInterface_jll v0.0.2+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [656ef2d0] OpenBLAS32_jll v0.3.34+0
  [458c3c95] OpenSSL_jll v3.5.8+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
  [36c8627f] Pango_jll v1.58.2+0
  [30392449] Pixman_jll v0.46.4+0
  [c0090381] Qt6Base_jll v6.10.2+2
  [629bc702] Qt6Declarative_jll v6.10.2+2
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
  [f50d1b31] Rmath_jll v0.5.2+0
  [ca45d3f4] SuiteSparse32_jll v7.12.1+1
  [fb77eaff] Sundials_jll v7.5.0+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
  [ffd25f8a] XZ_jll v5.8.4+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.4+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
  [a4ae2306] libaom_jll v3.14.1+0
  [0ac62f75] libass_jll v0.17.5+0
  [1183f4f0] libdecor_jll v0.2.2+0
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  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.58+0
  [9a156e7d] libva_jll v2.23.0+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
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  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
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  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

Chemical Akzo Nobel Differential-Algebraic Equation (DAE) Work-Precision Diagrams

High Tolerances

Timeseries Errors

Low Tolerances

Conclusion

Appendix