Support DomainSets 0.8 with MethodOfLines 0.11.14

[ChrisRackauckas-Claude]

Ignore until reviewed by @ChrisRackauckas.

Summary

This updates PDESystemLibrary for the MethodOfLines/DomainSets compatibility stack:

• allow DomainSets = "0.7.17, 0.8"
• require MethodOfLines = "0.11.14, 0.12"
• add the FunctionMaps dependency required by the DomainSets 0.8 stack
• fix heat_1d1 so the diffusion equation uses the second spatial derivative
• fix burgers_2d dependent-variable argument ordering to match [t, x, y]
• keep advdiff3 covered by using Rodas5P() for that example; FBDF() hits dt < eps on the third-order term under the new stack

MethodOfLines has had the source version bump to 0.11.14 merged, but as of this PR creation it was not yet tagged/registered. This PR is therefore based on the expected 0.11.14 release.

Validation

Run locally with MethodOfLines master, whose Project.toml is currently version 0.11.14:

using Pkg
Pkg.activate(; temp=true)
Pkg.develop(path=pwd())
Pkg.add(PackageSpec(name="MethodOfLines", url="https://github.com/SciML/MethodOfLines.jl", rev="master"))
Pkg.test("PDESystemLibrary")

Result:

Core/mol_test.jl | 426 passed, 1 broken, 427 total | 17m16.6s
Testing PDESystemLibrary tests passed

Also run:

Runic on changed Julia files
git diff --check

[ChrisRackauckas-Claude]

Downgrade follow-up: the initial CI failure was because the default Pkg server still only exposed MethodOfLines through 0.11.13, while General already has 0.11.14. Reproducing with direct registry access got past that and exposed a real lower-bound issue: ModelingToolkit 11.27 can select ModelingToolkitBase <= 1.48, which allows ImplicitDiscreteSolve 2.1.1 and fails on Julia 1.10 with too many parameters for type. Raising the MTK floor to 11.30.1 makes the downgraded stack select ModelingToolkitBase 1.51.0 and ImplicitDiscreteSolve 2.1.2.\n\nLocal validation in a clean worktree with direct registry access passed:\n\ntext\nCore/mol_test.jl | 426 passed, 1 broken, 427 total | 13m49.7s\nTesting PDESystemLibrary tests passed\n\n\nThe remaining CI risk is Pkg-server propagation for MethodOfLines 0.11.14; default Pkg server was still stale when checked locally after the failed CI run.

[ChrisRackauckas-Claude]

CI is still blocked on package-server registry propagation, not a new code failure. Fresh default/eager package-server Julia 1.10 depots still report MethodOfLines only through 0.11.13, so the PR's required 0.11.14 cannot resolve in GitHub Actions yet. Direct General does see and load MethodOfLines 0.11.14.

I also checked whether widening the test compat back to MethodOfLines 0.11.13 would be a valid workaround. It is not: with MethodOfLines 0.11.13 + DomainSets 0.8.1, Core/mol_test.jl starts running but errors in 19 examples, mostly convolution systems with missing initial conditions. So the 0.11.14 floor is real and should stay.

Current next step is to rerun/trigger CI once pkg.julialang.org's registry view includes MethodOfLines 0.11.14.