schroedinger example solution blows up

[aarontrowbridge]

Describe the bug 🐞

Schroedinger example fails out of the box -- but only requires simple fix in the bcs:

bcs = [
    ψ(0,x) => ψ0(x),
    ψ(t,xmin) ~ 0,
    ψ(t,xmax) ~ 0
]

Real problem is that solution seems to blow up:

Expected behavior

See gif in docs example

Minimal Reproducible Example 👇

Without MRE, we would only be able to help you to a limited extent, and attention to the issue would be limited. to know more about MRE refer to wikipedia and stackoverflow.

using MethodOfLines, OrdinaryDiffEq, Plots, DomainSets, ModelingToolkit

@parameters t, x
@variables ψ(..)

Dt = Differential(t)
Dxx = Differential(x)^2

xmin = 0
xmax = 1

V(x) = 0.0

eq = [im*Dt(ψ(t,x)) ~ Dxx(ψ(t,x)) + V(x)*ψ(t,x)] # You must enclose complex equations in a vector, even if there is only one equation

ψ0 = x -> sin(2pi*x)

ψ0(0.1)

bcs = [
    ψ(0,x) => ψ0(x),
    ψ(t,xmin) ~ 0,
    ψ(t,xmax) ~ 0
]

domains = [t ∈ Interval(0, 1), x ∈ Interval(xmin, xmax)]

@named sys = PDESystem(eq, bcs, domains, [t, x], [ψ(t,x)])

disc = MOLFiniteDifference([x => 100], t)

prob = discretize(sys, disc)

sol = solve(prob, TRBDF2(), saveat = 0.01)

discx = sol[x]
disct = sol[t]

discψ = sol[ψ(t, x)]
anim = @animate for i in 1:length(disct)
    u = discψ[i, :]
    plot(discx, [real.(u), imag.(u)], ylim = (-1.5, 1.5), title = "t = $(disct[i])", xlabel = "x", ylabel = "ψ(t,x)", label = ["re(ψ)" "im(ψ)"], legend = :topleft)
end
gif(anim, "schroedinger.gif", fps = 10)

Error & Stacktrace ⚠️

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

  [6e4b80f9] BenchmarkTools v1.6.0
  [052768ef] CUDA v5.6.1
  [13f3f980] CairoMakie v0.13.1
  [61c947e1] Clarabel v0.10.0
  [f65535da] Convex v0.16.4
  [071ae1c0] DiffEqGPU v3.4.1
  [0c46a032] DifferentialEquations v7.16.0
  [31c24e10] Distributions v0.25.117
  [5b8099bc] DomainSets v0.7.15
  [e24c0720] ExponentialAction v0.2.10
  [f6369f11] ForwardDiff v0.10.38
  [e9467ef8] GLMakie v0.11.2
  [7073ff75] IJulia v1.26.0
  [94925ecb] MethodOfLines v0.11.7
  [961ee093] ModelingToolkit v9.64.0
  [538bc3a1] NamedTrajectories v0.2.6
  [ab2f91bb] OSQP v0.8.1
  [5fb14364] OhMyREPL v0.5.28
  [1dea7af3] OrdinaryDiffEq v6.91.0
  [14b8a8f1] PkgTemplates v0.7.53
  [91a5bcdd] Plots v1.40.9
  [1fd47b50] QuadGK v2.11.2
  [6c2fb7c5] QuantumToolbox v0.27.0
  [189a3867] Reexport v1.2.2
  [295af30f] Revise v3.7.2
  [c946c3f1] SCS v2.0.2
  [90137ffa] StaticArrays v1.9.12
⌃ [0c5d862f] Symbolics v6.29.0
  [1c621080] TestItems v1.0.0
  [6dad8b7f] TrajectoryIndexingUtils v0.1.0

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `~/projects/JuliaPackages/Manifest.toml`
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  [276daf66] SpecialFunctions v2.5.0
  [860ef19b] StableRNGs v1.0.2
  [cae243ae] StackViews v0.1.1
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.12
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.4
  [4c63d2b9] StatsFuns v1.3.2
  [9672c7b4] SteadyStateDiffEq v2.4.1
  [789caeaf] StochasticDiffEq v6.74.0
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.1
  [09ab397b] StructArrays v0.7.0
  [856f2bd8] StructTypes v1.11.0
  [c3572dad] Sundials v4.26.1
  [2efcf032] SymbolicIndexingInterface v0.3.37
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.15.0
⌃ [0c5d862f] Symbolics v6.29.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [f8b46487] TestItemRunner v1.1.0
  [1c621080] TestItems v1.0.0
  [8290d209] ThreadingUtilities v0.5.2
  [731e570b] TiffImages v0.11.3
⌃ [a759f4b9] TimerOutputs v0.5.26
  [0796e94c] Tokenize v0.5.29
  [6356fb03] TrajectoryBundles v0.1.0 `TrajectoryBundles.jl`
  [6dad8b7f] TrajectoryIndexingUtils v0.1.0
  [3bb67fe8] TranscodingStreams v0.11.3
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.10
  [981d1d27] TriplotBase v0.1.0
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [967fb449] Unidecode v1.1.0
  [1986cc42] Unitful v1.22.0
  [45397f5d] UnitfulLatexify v1.6.4
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.3.0
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.71
  [81def892] VersionParsing v1.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
  [897b6980] WeakValueDicts v0.1.0
  [e3aaa7dc] WebP v0.1.3
  [efce3f68] WoodburyMatrices v1.0.0
  [c2297ded] ZMQ v1.4.0
  [700de1a5] ZygoteRules v0.2.7
  [ae81ac8f] ASL_jll v0.1.3+0
  [6e34b625] Bzip2_jll v1.0.9+0
  [4e9b3aee] CRlibm_jll v1.0.1+0
⌅ [4ee394cb] CUDA_Driver_jll v0.10.4+0
⌅ [76a88914] CUDA_Runtime_jll v0.15.5+0
  [83423d85] Cairo_jll v1.18.2+1
  [ee1fde0b] Dbus_jll v1.14.10+0
  [5ae413db] EarCut_jll v2.2.4+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.6.5+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [f5851436] FFTW_jll v3.3.10+3
  [a3f928ae] Fontconfig_jll v2.15.0+0
  [d7e528f0] FreeType2_jll v2.13.3+1
  [559328eb] FriBidi_jll v1.0.16+0
  [0656b61e] GLFW_jll v3.4.0+2
  [d2c73de3] GR_jll v0.73.13+0
  [78b55507] Gettext_jll v0.21.0+0
  [59f7168a] Giflib_jll v5.2.3+0
  [7746bdde] Glib_jll v2.82.4+0
  [3b182d85] Graphite2_jll v1.3.14+1
  [017b0a0e] HSL_jll v4.0.2+0
  [2e76f6c2] HarfBuzz_jll v8.5.0+0
⌃ [e33a78d0] Hwloc_jll v2.11.2+3
  [905a6f67] Imath_jll v3.1.11+0
⌅ [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
  [9cc047cb] Ipopt_jll v300.1400.1700+0
  [aacddb02] JpegTurbo_jll v3.1.1+0
  [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.1+0
  [dad2f222] LLVMExtra_jll v0.0.35+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.3+0
⌅ [e9f186c6] Libffi_jll v3.2.2+2
  [d4300ac3] Libgcrypt_jll v1.11.0+0
  [7e76a0d4] Libglvnd_jll v1.7.0+0
  [7add5ba3] Libgpg_error_jll v1.51.1+0
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.40.3+0
  [89763e89] Libtiff_jll v4.7.1+0
  [38a345b3] Libuuid_jll v2.40.3+0
  [d00139f3] METIS_jll v5.1.3+0
⌅ [856f044c] MKL_jll v2024.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.700.301+0
⌃ [e98f9f5b] NVTX_jll v3.1.0+2
  [9c4f68bf] OSQP_jll v0.600.200+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [656ef2d0] OpenBLAS32_jll v0.3.29+0
  [18a262bb] OpenEXR_jll v3.2.4+0
  [458c3c95] OpenSSL_jll v3.0.16+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.56.1+0
⌅ [30392449] Pixman_jll v0.43.4+0
⌅ [c0090381] Qt6Base_jll v6.7.1+1
⌅ [629bc702] Qt6Declarative_jll v6.7.1+2
⌅ [ce943373] Qt6ShaderTools_jll v6.7.1+1
⌃ [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.5.1+0
  [f4f2fc5b] SCS_jll v3.2.7+0
⌅ [319450e9] SPRAL_jll v2024.5.8+0
⌅ [fb77eaff] Sundials_jll v5.2.3+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+2
  [2381bf8a] Wayland_protocols_jll v1.36.0+0
  [02c8fc9c] XML2_jll v2.13.6+0
  [aed1982a] XSLT_jll v1.1.42+0
  [ffd25f8a] XZ_jll v5.6.4+1
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+3
  [0c0b7dd1] Xorg_libXau_jll v1.0.12+0
  [935fb764] Xorg_libXcursor_jll v1.2.3+0
  [a3789734] Xorg_libXdmcp_jll v1.1.5+0
  [1082639a] Xorg_libXext_jll v1.3.6+3
  [d091e8ba] Xorg_libXfixes_jll v6.0.0+0
  [a51aa0fd] Xorg_libXi_jll v1.8.2+0
  [d1454406] Xorg_libXinerama_jll v1.1.5+0
  [ec84b674] Xorg_libXrandr_jll v1.5.4+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+1
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.2+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+3
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+1
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+1
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.1+0
  [8f1865be] ZeroMQ_jll v4.3.5+3
  [3161d3a3] Zstd_jll v1.5.7+0
  [1e29f10c] demumble_jll v1.3.0+0
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.56.3+0
  [1a1c6b14] gperf_jll v3.1.1+1
  [9a68df92] isoband_jll v0.2.3+0
  [a4ae2306] libaom_jll v3.11.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.46+0
  [075b6546] libsixel_jll v1.10.5+0
  [a9144af2] libsodium_jll v1.0.20+3
  [f27f6e37] libvorbis_jll v1.3.7+2
  [c5f90fcd] libwebp_jll v1.5.0+0
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+2
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [8bf52ea8] CRC32c 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
  [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 v1.11.0
  [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
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.1+2
  [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

• Output of versioninfo()

Julia Version 1.11.3
Commit d63adeda50d (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 24 × 12th Gen Intel(R) Core(TM) i9-12900KS
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 1 default, 0 interactive, 1 GC (on 24 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 

Additional context

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