Kenneth ChengMathematical modeling

Editorial project overview

One Integrator Across the Fast-Slow Boundary

Can one simple linearly implicit update preserve proved structure and the correct fixed-step slow limit across a frozen stiffness grid without implying error or runtime superiority?

Reproducible studyUpdated 30 Aug 2026
Technical figure from One Integrator Across the Fast-Slow Boundary
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Editorial overview

The literature gate returned REFRAME because Michaelis-Menten singular perturbations, IMEX/AP error analysis, uniformly accurate conditions and positive conservative kinetics integrators are established. Kaiser and Schutz (2018) directly overlaps the proposed method headline.

Read One Integrator Across the Fast-Slow Boundary for the model, update equations, algebraic property audit, tightened Radau reference, frozen error grid, preserved backward-Euler comparison null, RK4 failures, reduced-model boundary and reproduction record.

Key findings

  • The closed-form linearly implicit update analytically preserves the exact weighted invariant, remains nonnegative with c at most one, and has the correct fixed-step epsilon-to-zero update.
  • The minimum last-pair order is 0.7885, the maximum fixed-step AP-limit discrepancy is 3.4480e-7, and the finest-step uniform weighted-error envelope is 0.0053654 on the frozen grid.
  • The comparative hypothesis is null: AP error exceeds backward-Euler error at every frozen epsilon by factors from 1.0143 to 2.0444; RK4 fails or becomes nonphysical in 28/40 fixed cases.

Limitations

  • The evidence covers one synthetic dimensionless irreversible Michaelis-Menten family, ten epsilon values, four fixed steps and one ill-prepared initial condition.
  • The project introduces no new AP/IMEX solver or uniform-accuracy theorem and contains no external Radau/BDF/VODE work-precision comparison.
  • There is no biochemical parameter fit, experiment, biological validation, clinical claim or runtime-superiority result.

Technical record

Detailed source, calculations, generated figures, and reproduction instructions are maintained in a private technical workspace. Public articles contain only manually reviewed interpretation and approved figures.

Version history

2026-08-30 — Curated overview reviewed against repository evidence.