[rogeriojorge]

Summary

• replace SPECTRAX's private Newton–GMRES loop with SOLVAX's matrix-free newton_krylov
• expose separate nonlinear and linear residual tolerances on ImplicitMidpoint
• remove 43 net source lines; the released SOLVAX dependency is supplied by Use SOLVAX Newton-Krylov with a Hermite line preconditioner in implicit midpoint #21

This retains the midpoint rule, step limits, Krylov restart controls, and Diffrax failure result. The simplified PR now changes only midpoint_solver.py.

Why

SOLVAX owns the generic PyTree Newton–Krylov implementation, including true final residual checks and linear-solve diagnostics. Keeping a second nonlinear solver in SPECTRAX duplicates logic and makes preconditioning and distributed inner products harder to maintain.

The nonlinear stopping criterion is:

||F|| <= max(atol, rtol * ||F_initial||)

linear_rtol and linear_atol independently control each GMRES solve. The former SOLVAX #14 prerequisite is included in released SOLVAX 0.8.x.

Validation

• complete top-of-stack tests against the released SOLVAX 0.8.3 wheel: 9 passed
• ruff check spectrax/midpoint_solver.py
• ruff format --check spectrax/midpoint_solver.py
• source and wheel builds
• 65² Fourier, 28x4x4 Hermite, 20 midpoint steps:
  • relative endpoint difference from Evaluate implicit RHS at midpoint time #26: 3.50e-11 in Ck, 6.38e-11 in Fk
  • energy drift: 2.51e-14 (Evaluate implicit RHS at midpoint time #26) versus 1.21e-16 (this PR)
  • warm runtime: 7.51 s (Evaluate implicit RHS at midpoint time #26) versus 10.88 s (this PR)

The additional cost is the initial reference and true final residual evaluation. The collision/diffusion preconditioner remains a separate follow-up rather than weakening convergence reporting here.

[rogeriojorge]

Squashed into #21.