Update for OrdinaryDiffEq v7 / DifferentialEquations v8

[ChrisRackauckas-Claude]

Summary

Updates the package for the OrdinaryDiffEq v7 / DifferentialEquations v8 breaking release. Three small changes are sufficient — FNC only uses ODE features, so most of the v7 surface (controllers, ADTypes, ODEAliasSpecifier, ODEVerbosity, callback signatures, ensemble RNG, …) doesn't apply here.

Changes

1. Project.toml — bumped DifferentialEquations compat from "7.15" to "7.15, 8". The umbrella package was scoped down in v8 to only re-export OrdinaryDiffEq, but every call site in this repo is ODE-only (Tsit5, ODEProblem, solve), so existing usage continues to work after the bump.

2. src/chapter10.jl — fixed one indexing breakage in shoot. Under RecursiveArrayTools v4 (shipped with OrdinaryDiffEq v7), ODESolution now subtypes AbstractArray, so sol[end] returns the last scalar element in column-major order rather than the last timestep vector. The downstream g₂(y[end]...) then tries to splat a Float64 and errors. Switched to y.u[end]..., which is the forward-compatible form (works under both RAT v3 and v4).

   The companion y[1,:], y[2,:] lines from commit e15d935 still work unchanged: AbstractArray row-slicing on the (ncomponents, ntimesteps) column-major storage returns the same per-component trajectories as the v3 override did. I verified this empirically against OrdinaryDiffEq v7.0.0 before deciding to leave them.

3. README.md — updated the "alternative numerical packages" table to point BVP users at BoundaryValueDiffEq directly. DifferentialEquations v8 no longer re-exports the BVP solver family from the umbrella, so the old recommendation would no longer give the user a working BVP setup.

Why this is the whole diff

I read the OrdinaryDiffEq v7 / DiffEq v8 NEWS.md end-to-end and audited the repo for every category of breaking change:

v7/v8 breaking change	Affects FNC?
DiffEq v8 umbrella reduction (only re-exports OrdinaryDiffEq)	No — only ODE features used
RAT v4 sol[i] → sol.u[i]	Yes — fixed in chapter10.jl
sol[1,:] / sol[2,:] row slicing	No — semantics preserved on AbstractArray
for u in sol, length(sol), eachindex(sol)	No — not used
sol.retcode == :Symbol	No — retcode not inspected
sol.destats → sol.stats	No — not used
u_modified! → derivative_discontinuity!	No — no callbacks
autodiff::Bool → ADTypes	No — implicit solvers / autodiff kwargs not used
verbose::Bool → ODEVerbosity	No
alias::Bool / alias_u0 → ODEAliasSpecifier	No
gamma/beta1/beta2/q* controller kwargs → controller=	No
chunk_size/diff_type/standardtag/precs algorithm kwargs	No
lazy::Bool → Val{true/false}	No
williamson_condition=true default → false	No (no 2N low-storage RKs)
VectorContinuousCallback affect! signature	No
CheckInit default DAE init	No (no DAEs)
Tableau construct* rename	No
Threading: Static.True/False → Serial/Threaded	No
Algorithm struct {CS,AD,FDT,ST,CJ} type-param removal	No
Ensemble prob_func/output_func signature	No
KenCarp4/Rodas4/etc. now require explicit sublib	No (only Tsit5 used)

The only call site touched in src/ is the shoot function. Everything else in the repo (euler, ie2, rk4, rk23, ab4, am2 in chapter06, parabolic in chapter11) operates on user-written RHS functions or uses solve(ivp) with default-solver behavior, both of which are unchanged.

Test plan

• Resolve and precompile FNC against DifferentialEquations v8.0.0 / OrdinaryDiffEq v7.0.0 on Julia 1.11

• Pkg.test() — all 11 test sets pass (74 total tests):

  Chapter 1   |  1   1   0.6s
  Chapter 2   |  8   8   4.7s
  Chapter 3   |  4   4   4.2s
  Chapter 4   | 11  11   1.4s
  Chapter 5   | 12  12   4.4s
  Chapter 6   |  8   8   4.8s   <- exercises Tsit5 + euler/ie2/rk4/ab4/rk23/am2
  Chapter 8   |  7   7   1.8s
  Chapter 9   |  7   7   4.8s
  Chapter 10  |  8   8   9.5s   <- exercises shoot, bvplin, bvp, fem
  Chapter 11  |  5   5  28.8s   <- exercises parabolic (solve(ivp))
  Chapter 13  |  3   3  17.2s
       Testing FundamentalsNumericalComputation tests passed
  

• Empirically verified RAT v4 indexing semantics (sol[1,:] and sol[2,:] return per-component trajectories; sol[end] returns a scalar; sol.u[end] returns the last timestep vector) before deciding which lines actually needed migration.

[ChrisRackauckas]

Both versions are still supported.

[ChrisRackauckas]

The other BVP docs are sub-docs here, so the full thing is better. Therefore this is good.

[ChrisRackauckas]

You probably shouldn't splat for performance, but this at least matches before.

[ChrisRackauckas]

This is a reasonably backwards compatible change.