Lax equivalence theorem

{
  "id": "MLC-T-MET-006894",
  "term": "Lax equivalence theorem",
  "field": "Meteorology and atmospheric science",
  "definition": "A foundational principle in the numerical analysis of partial differential equations, stating that for a consistent finite-difference scheme, stability is the necessary and sufficient condition for convergence. In numerical weather prediction, this theorem provides the theoretical basis for developing stable and accurate models. It connects the mathematical properties of a numerical method to its ability to produce a solution that approaches the true atmospheric state as grid resolution increases.",
  "see_also": [
    "stability"
  ],
  "url": "https://mlchart.com/terminology/meteorology/lax-equivalence-theorem/"
}