GitHub

Orbital Dynamics BVP Benchmark

This is a benchmark of a small non-stiff BVP.

using BoundaryValueDiffEq, OrdinaryDiffEq, BenchmarkTools

y0 = [
    -4.7763169762853989E+06,
    -3.8386398704441520E+05,
    -5.3500183933132319E+06,
    -5528.612564911408,
    1216.8442360202787,
    4845.114446429901
]
init_val = [
    -4.7763169762853989E+06,
    -3.8386398704441520E+05,
    -5.3500183933132319E+06,
    7.0526926403748598E+06,
    -7.9650476230388973E+05,
    -1.1911128863666430E+06
]
J2 = 1.08262668E-3
req = 6378137
myu = 398600.4418E+9
t0 = 86400 * 2.3577475462484435E+04
t1 = 86400 * 2.3577522023524125E+04
tspan = (t0, t1)

# ODE solver
function orbital(dy, y, p, t)
    r2 = (y[1]^2 + y[2]^2 + y[3]^2)
    r3 = r2^(3 / 2)
    w = 1 + 1.5J2 * (req * req / r2) * (1 - 5y[3] * y[3] / r2)
    w2 = 1 + 1.5J2 * (req * req / r2) * (3 - 5y[3] * y[3] / r2)
    dy[1] = y[4]
    dy[2] = y[5]
    dy[3] = y[6]
    dy[4] = -myu * y[1] * w / r3
    dy[5] = -myu * y[2] * w / r3
    dy[6] = -myu * y[3] * w2 / r3
end

function bc!_generator(resid, sol, init_val)
    resid[1] = sol[1][1] - init_val[1]
    resid[2] = sol[1][2] - init_val[2]
    resid[3] = sol[1][3] - init_val[3]
    resid[4] = sol[end][1] - init_val[4]
    resid[5] = sol[end][2] - init_val[5]
    resid[6] = sol[end][3] - init_val[6]
end
cur_bc! = (resid, sol, p, t) -> bc!_generator(resid, sol, init_val)
resid_f = Array{Float64}(undef, 6)
bvp = BVProblem(orbital, cur_bc!, y0, tspan)
BVProblem with uType Vector{Float64} and tType Float64. In-place: true
Non-trivial mass matrix: false
timespan: (2.037093879958655e9, 2.0370979028324845e9)
u0: 6-element Vector{Float64}:
      -4.776316976285399e6
 -383863.9870444152
      -5.350018393313232e6
   -5528.612564911408
    1216.8442360202787
    4845.114446429901
@btime sol = solve(bvp, Shooting(DP5()), abstol = 1e-13, reltol = 1e-13)
13.731 s (167853623 allocations: 5.31 GiB)
retcode: MaxIters
Interpolation: specialized 4th order "free" interpolation
t: 355-element Vector{Float64}:
 2.037093879958655e9
 2.0370938799641182e9
 2.0370938801536946e9
 2.0370938820494595e9
 2.0370938884725344e9
 2.037093896188355e9
 2.0370939060108583e9
 2.037093916577122e9
 2.037093927788337e9
 2.0370939392661736e9
 ⋮
 2.0370978148025277e9
 2.0370978258596663e9
 2.0370978369346879e9
 2.0370978480277495e9
 2.037097859138979e9
 2.0370978702684672e9
 2.037097881416288e9
 2.037097892582501e9
 2.0370979028324845e9
u: 355-element Vector{Vector{Float64}}:
 [-4.776316976285399e6, -383863.9870444152, -5.350018393313232e6, -5528.612
563833361, 1216.844236150994, 4845.114447414833]
 [-4.776347179792938e6, -383857.3392479316, -5.349991923689108e6, -5528.584
553164405, 1216.8464872913637, 4845.14590292104]
 [-4.777395177323275e6, -383626.64635520446, -5.349073294461405e6, -5527.61
24443342205, 1216.924580035703, 4846.237345036243]
 [-4.787865008916723e6, -381318.90488838113, -5.339875628840166e6, -5517.87
9578391214, 1217.7029292187503, 4857.141511082623]
 [-4.823200480239278e6, -373489.12159798393, -5.308559527316557e6, -5484.74
4711058072, 1220.3051861501083, 4893.9470300930625]
 [-4.865365208241111e6, -364061.631002387, -5.2706290405571265e6, -5444.618
366739416, 1223.3598397377045, 4937.87446661069]
 [-4.918592091240459e6, -352026.5277837376, -5.221853927200201e6, -5393.030
61182338, 1227.1355484911037, 4993.34006020117]
 [-4.975280351464576e6, -339039.4511315414, -5.168780272886336e6, -5336.910
061909664, 1231.0554488188252, 5052.429638884964]
 [-5.034776538937267e6, -325215.2570047803, -5.11178800957856e6, -5276.6611
66675213, 1235.0534882060672, 5114.465497644278]
 [-5.094983665606321e6, -311016.8473214559, -5.052723923634035e6, -5214.238
069876669, 1238.9741700520642, 5177.263483726902]
 ⋮
 [7.141536420715977e6, -707641.7356181318, -548487.8868795035, -673.9317021
336685, -1044.2244365209708, -7336.126144217646]
 [7.133617536950343e6, -719141.3151572072, -629566.6959791188, -758.4097614
975759, -1035.7809642328307, -7329.136845806945]
 [7.124750023799057e6, -730565.1519364676, -710693.829715777, -842.92666369
98791, -1027.1877853424737, -7321.17217088596]
 [7.114930347144678e6, -741911.443337747, -791859.3301786431, -927.47192045
90832, -1018.4452495655219, -7312.228332492408]
 [7.104155078282119e6, -753178.3486399926, -873052.9245025575, -1012.034715
8012074, -1009.55375117218, -7302.301649791317]
 [7.092420915943856e6, -764363.9835322388, -954263.975567688, -1096.6038549
87601, -1000.5137367545303, -7291.388570056695]
 [7.079724680660449e6, -775466.441276869, -1.0354816260193476e6, -1181.1679
147639295, -991.3256915147424, -7279.485664948177]
 [7.066063320460638e6, -786483.7964118784, -1.1166948195764285e6, -1265.715
2657476738, -981.9901382327375, -7266.589636698655]
 [7.052692640384875e6, -796504.7622966168, -1.1911128863124591e6, -1343.177
8200835643, -973.305071397493, -7253.895584501203]
dt = (t1 - t0) / 100
@btime sol = solve(bvp, MIRK2(), dt = $dt, abstol = 1e-13, reltol = 1e-13)
20.625 s (224184450 allocations: 5.87 GiB)
retcode: Unstable
Interpolation: MIRK Order 2 Interpolation
t: 1617-element Vector{Float64}:
 2.037093879958655e9
 2.0370938824480572e9
 2.0370938849374595e9
 2.0370938874268615e9
 2.0370938899162636e9
 2.0370938924056656e9
 2.0370938948950677e9
 2.03709389738447e9
 2.037093899873872e9
 2.037093902363274e9
 ⋮
 2.0370978829172676e9
 2.0370978854066696e9
 2.037097887896072e9
 2.037097890385474e9
 2.037097892874876e9
 2.037097895364278e9
 2.0370978978536801e9
 2.0370979003430824e9
 2.0370979028324845e9
u: 1617-element Vector{Vector{Float64}}:
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 ⋮
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
@btime sol = solve(bvp, MIRK3(), dt = $dt, abstol = 1e-13, reltol = 1e-13)
27.471 s (334863585 allocations: 7.81 GiB)
retcode: Unstable
Interpolation: MIRK Order 3 Interpolation
t: 1617-element Vector{Float64}:
 2.037093879958655e9
 2.0370938824480572e9
 2.0370938849374595e9
 2.0370938874268615e9
 2.0370938899162636e9
 2.0370938924056656e9
 2.0370938948950677e9
 2.03709389738447e9
 2.037093899873872e9
 2.037093902363274e9
 ⋮
 2.0370978829172676e9
 2.0370978854066696e9
 2.037097887896072e9
 2.037097890385474e9
 2.037097892874876e9
 2.037097895364278e9
 2.0370978978536801e9
 2.0370979003430824e9
 2.0370979028324845e9
u: 1617-element Vector{Vector{Float64}}:
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 ⋮
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
@btime sol = solve(bvp, MIRK4(), dt = $dt, abstol = 1e-13, reltol = 1e-13)
34.448 s (448797445 allocations: 9.90 GiB)
retcode: Unstable
Interpolation: MIRK Order 4 Interpolation
t: 1617-element Vector{Float64}:
 2.037093879958655e9
 2.0370938824480572e9
 2.0370938849374595e9
 2.0370938874268615e9
 2.0370938899162636e9
 2.0370938924056656e9
 2.0370938948950677e9
 2.03709389738447e9
 2.037093899873872e9
 2.037093902363274e9
 ⋮
 2.0370978829172676e9
 2.0370978854066696e9
 2.037097887896072e9
 2.037097890385474e9
 2.037097892874876e9
 2.037097895364278e9
 2.0370978978536801e9
 2.0370979003430824e9
 2.0370979028324845e9
u: 1617-element Vector{Vector{Float64}}:
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 ⋮
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
@btime sol = solve(bvp, MIRK5(), dt = $dt, abstol = 1e-13, reltol = 1e-13)
41.201 s (559708206 allocations: 11.86 GiB)
retcode: Unstable
Interpolation: MIRK Order 5 Interpolation
t: 1617-element Vector{Float64}:
 2.037093879958655e9
 2.0370938824480572e9
 2.0370938849374595e9
 2.0370938874268615e9
 2.0370938899162636e9
 2.0370938924056656e9
 2.0370938948950677e9
 2.03709389738447e9
 2.037093899873872e9
 2.037093902363274e9
 ⋮
 2.0370978829172676e9
 2.0370978854066696e9
 2.037097887896072e9
 2.037097890385474e9
 2.037097892874876e9
 2.037097895364278e9
 2.0370978978536801e9
 2.0370979003430824e9
 2.0370979028324845e9
u: 1617-element Vector{Vector{Float64}}:
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 ⋮
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
@btime sol = solve(bvp, MIRK6(), dt = $dt, abstol = 1e-13, reltol = 1e-13)
49.099 s (676883854 allocations: 14.08 GiB)
retcode: Unstable
Interpolation: MIRK Order 6 Interpolation
t: 1617-element Vector{Float64}:
 2.037093879958655e9
 2.0370938824480572e9
 2.0370938849374595e9
 2.0370938874268615e9
 2.0370938899162636e9
 2.0370938924056656e9
 2.0370938948950677e9
 2.03709389738447e9
 2.037093899873872e9
 2.037093902363274e9
 ⋮
 2.0370978829172676e9
 2.0370978854066696e9
 2.037097887896072e9
 2.037097890385474e9
 2.037097892874876e9
 2.037097895364278e9
 2.0370978978536801e9
 2.0370979003430824e9
 2.0370979028324845e9
u: 1617-element Vector{Vector{Float64}}:
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 ⋮
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

Appendix

Appendix

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/NonStiffBVP","orbital.jmd")

Computer Information:

Julia Version 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 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-18.1.7 (ORCJIT, znver2)
  GC: Built with stock GC
Threads: 128 default, 1 interactive, 128 GC (on 128 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

Package Information:

Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/NonStiffBVP/Project.toml`
  [ded0fc24] BVProblemLibrary v0.1.8
⌃ [6e4b80f9] BenchmarkTools v1.6.3
  [764a87c0] BoundaryValueDiffEq v5.20.0
  [13f3f980] CairoMakie v0.15.9
  [f3b72e0c] DiffEqDevTools v2.51.0
⌅ [5959db7a] NonlinearSolveFirstOrder v1.11.1
  [54ca160b] ODEInterface v0.5.0
⌃ [1dea7af3] OrdinaryDiffEq v6.108.0
  [91a5bcdd] Plots v1.41.6
  [31c91b34] SciMLBenchmarks v0.1.3 [loaded: v0.1.4]
  [be0294bd] SimpleBoundaryValueDiffEq v1.2.0
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/NonStiffBVP/Manifest.toml`
  [47edcb42] ADTypes v1.21.0
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.44
  [79e6a3ab] Adapt v4.5.0
  [35492f91] AdaptivePredicates v1.2.0
  [66dad0bd] AliasTables v1.1.3
  [a95523ee] AlmostBlockDiagonals v0.1.10
  [27a7e980] Animations v0.4.2
  [4fba245c] ArrayInterface v7.23.0
  [4c555306] ArrayLayouts v1.12.2
  [67c07d97] Automa v1.1.0
  [13072b0f] AxisAlgorithms v1.1.0
  [39de3d68] AxisArrays v0.4.8
  [ded0fc24] BVProblemLibrary v0.1.8
  [aae01518] BandedMatrices v1.11.0
  [18cc8868] BaseDirs v1.3.2
⌃ [6e4b80f9] BenchmarkTools v1.6.3
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [764a87c0] BoundaryValueDiffEq v5.20.0
⌃ [7227322d] BoundaryValueDiffEqAscher v1.11.0
⌃ [56b672f2] BoundaryValueDiffEqCore v2.1.0
⌃ [85d9eb09] BoundaryValueDiffEqFIRK v1.12.0
⌃ [1a22d4ce] BoundaryValueDiffEqMIRK v1.12.0
⌃ [9255f1d6] BoundaryValueDiffEqMIRKN v1.11.0
⌃ [ed55bfe0] BoundaryValueDiffEqShooting v1.12.0
⌃ [70df07ce] BracketingNonlinearSolve v1.11.0
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⌃ [d360d2e6] ChainRulesCore v1.26.0
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  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
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⌃ [864edb3b] DataStructures v0.19.3
  [e2d170a0] DataValueInterfaces v1.0.0
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⌃ [2b5f629d] DiffEqBase v6.211.0
  [f3b72e0c] DiffEqDevTools v2.51.0
⌃ [77a26b50] DiffEqNoiseProcess v5.27.0
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⌃ [f151be2c] EnzymeCore v0.8.18
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⌅ [7034ab61] FastBroadcast v0.3.5
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  [442a2c76] FastGaussQuadrature v1.1.0
  [a4df4552] FastPower v1.3.1
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⌅ [77dc65aa] FunctionWrappersWrappers v0.1.3
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  [c145ed77] GenericSchur v0.5.6
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  [42e2da0e] Grisu v1.0.2
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  [cd3eb016] HTTP v1.11.0
⌅ [eafb193a] Highlights v0.5.3
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⌃ [de52edbc] Integrals v5.1.0
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⌃ [d1acc4aa] IntervalArithmetic v1.0.3
⌃ [8197267c] IntervalSets v0.7.13
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  [f1662d9f] Isoband v0.1.1
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  [1019f520] JLFzf v0.1.11
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⌅ [682c06a0] JSON v0.21.4
  [ae98c720] Jieko v0.2.1
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⌃ [5078a376] LazyArrays v2.9.5
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  [d3d80556] LineSearches v7.6.0
⌃ [7ed4a6bd] LinearSolve v3.68.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
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  [4886b29c] MonteCarloIntegration v0.2.0
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  [77ba4419] NaNMath v1.1.3
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⌃ [8913a72c] NonlinearSolve v4.15.0
⌃ [be0214bd] NonlinearSolveBase v2.16.0
⌅ [5959db7a] NonlinearSolveFirstOrder v1.11.1
⌃ [9a2c21bd] NonlinearSolveQuasiNewton v1.12.0
⌃ [26075421] NonlinearSolveSpectralMethods v1.6.0
  [54ca160b] ODEInterface v0.5.0
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  [52e1d378] OpenEXR v0.3.3
  [4d8831e6] OpenSSL v1.6.1
  [bca83a33] OptimizationBase v5.1.0
  [bac558e1] OrderedCollections v1.8.1
⌃ [1dea7af3] OrdinaryDiffEq v6.108.0
⌃ [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.10.0
⌃ [6ad6398a] OrdinaryDiffEqBDF v1.23.0
⌃ [bbf590c4] OrdinaryDiffEqCore v3.23.0
  [50262376] OrdinaryDiffEqDefault v1.14.0
⌃ [4302a76b] OrdinaryDiffEqDifferentiation v2.3.0
⌃ [9286f039] OrdinaryDiffEqExplicitRK v1.10.0
⌃ [e0540318] OrdinaryDiffEqExponentialRK v1.14.0
⌃ [becaefa8] OrdinaryDiffEqExtrapolation v1.17.0
⌃ [5960d6e9] OrdinaryDiffEqFIRK v1.24.0
⌃ [101fe9f7] OrdinaryDiffEqFeagin v1.9.0
⌃ [d3585ca7] OrdinaryDiffEqFunctionMap v1.10.0
⌃ [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.10.0
⌃ [9f002381] OrdinaryDiffEqIMEXMultistep v1.13.0
⌃ [521117fe] OrdinaryDiffEqLinear v1.11.0
⌃ [1344f307] OrdinaryDiffEqLowOrderRK v1.11.0
⌃ [b0944070] OrdinaryDiffEqLowStorageRK v1.13.0
⌃ [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.24.0
⌃ [c9986a66] OrdinaryDiffEqNordsieck v1.10.0
⌃ [5dd0a6cf] OrdinaryDiffEqPDIRK v1.12.0
⌃ [5b33eab2] OrdinaryDiffEqPRK v1.9.0
⌃ [04162be5] OrdinaryDiffEqQPRK v1.9.0
⌃ [af6ede74] OrdinaryDiffEqRKN v1.11.0
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v1.26.0
⌃ [2d112036] OrdinaryDiffEqSDIRK v1.13.0
⌃ [669c94d9] OrdinaryDiffEqSSPRK v1.12.0
⌃ [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.12.0
⌃ [358294b1] OrdinaryDiffEqStabilizedRK v1.9.0
⌃ [fa646aed] OrdinaryDiffEqSymplecticRK v1.12.0
⌃ [b1df2697] OrdinaryDiffEqTsit5 v1.10.0
⌃ [79d7bb75] OrdinaryDiffEqVerner v1.12.0
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⌃ [1fd47b50] QuadGK v2.11.2
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⌃ [c0aeaf25] SciMLOperators v1.15.1
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⌃ [83423d85] Cairo_jll v1.18.5+1
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⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
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  [2e76f6c2] HarfBuzz_jll v8.5.1+0
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⌅ [e9f186c6] Libffi_jll v3.4.7+0
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  [856f044c] MKL_jll v2025.2.0+0
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  [e7412a2a] Ogg_jll v1.3.6+0
  [6cdc7f73] OpenBLASConsistentFPCSR_jll v0.3.30+0
⌃ [18a262bb] OpenEXR_jll v3.4.4+0
⌃ [9bd350c2] OpenSSH_jll v10.2.1+0
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  [91d4177d] Opus_jll v1.6.1+0
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⌅ [30392449] Pixman_jll v0.44.2+0
  [c0090381] Qt6Base_jll v6.10.2+1
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  [a2964d1f] Wayland_jll v1.24.0+0
⌃ [ffd25f8a] XZ_jll v5.8.2+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
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  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
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  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
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⌃ [b53b4c65] libpng_jll v1.6.55+0
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⌅ [1270edf5] x264_jll v10164.0.1+0
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  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [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 v1.3.0+1
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.11.4
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.4+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0
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`