Kenneth ChengMathematical modeling

Editorial project overview

Positive and Conservative Time Stepping

When do standard explicit schemes create negative states, and what accuracy is traded for feasibility?

Reproducible studyUpdated 28 Jul 2026
Technical figure from Positive and Conservative Time Stepping
A reviewed research figure synchronized from the private technical workspace. The original aspect ratio and labels are preserved.

Editorial overview

The benchmark distinguishes algebraic conservation, computed conservation, positivity, and accuracy. Read When a Numerical Method Creates Negative Matter.

Key findings

  • Euler is negative in 38.46% and RK4 in 25.17% of 429 tested cases.
  • The positive implicit method has zero negative cases and mass drift below 9e-14.

Limitations

  • Linear conservative transfer networks only.
  • No universal comparison with all high-order structure-preserving solvers.

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

2026-07-28 — Curated overview reviewed against repository evidence.