Convergent numerical scheme

{
  "id": "MLC-T-MET-004687",
  "term": "Convergent numerical scheme",
  "field": "Meteorology and atmospheric science",
  "definition": "A numerical method for solving differential equations where the numerical solution approaches the true analytical solution as the grid spacing or time step approaches zero. For a scheme to be convergent in practice, it must be both consistent with the original equation and numerically stable. The Lax equivalence theorem states that for a linear problem, a consistent scheme is convergent if and only if it is stable.",
  "see_also": [
    "Lax equivalence theorem",
    "consistent numerical scheme",
    "stability"
  ],
  "url": "https://mlchart.com/terminology/meteorology/convergent-numerical-scheme/"
}