{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "1RGPVZXVD9"
    },
    {
      "field": "uses",
      "target": "559N53ZTMV"
    },
    {
      "field": "uses",
      "target": "5R9ZRK8YB5"
    },
    {
      "field": "uses",
      "target": "MM0YNN1MJA"
    },
    {
      "field": "uses",
      "target": "ZR1DPX6VAN"
    },
    {
      "field": "defines",
      "target": "J8ZRM7KFJH"
    }
  ],
  "body": "\n## Summary\n\nThe Lax–Wendroff method is an explicit [[finite difference|X7HYEBA5SA]] scheme of second order in space and time for hyperbolic equations and [[conservation laws|8RA7AMWSAF]].\nIt comes from a Taylor expansion in time in which the time derivatives are replaced by space derivatives using the equation.\nIt is stable under the CFL condition and accurate for smooth solutions, but it produces oscillations next to discontinuities.\nThis is why it is often combined with a first-order scheme through a flux limiter.\n\n## Explanations\n\n### L1 human\n\nFor the [[transport equation|PVD7VZJZ9B]] $u_t + a u_x = 0$, the value at the next time is $u + \\Delta t\\, u_t + \\frac{\\Delta t^2}{2} u_{tt}$ up to higher terms.\nThe equation says $u_t = -a u_x$ and $u_{tt} = a^2 u_{xx}$, so one only needs space derivatives, and these are replaced by centred differences.\nThe result uses three neighbouring grid values and is accurate to second order.\nNear a jump, it overshoots and undershoots, creating small wiggles.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "65M06",
      "35L65"
    ],
    "name": "Lax–Wendroff method",
    "same_as": {
      "wikidata": "Q259958",
      "wikipedia": "Lax–Wendroff method"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Lax%E2%80%93Wendroff_method"
      }
    ],
    "specializes": [
      "X7HYEBA5SA"
    ],
    "tag": "YHZ9BCNDRZ"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/YHZ9BCNDRZ/",
  "links": [
    {
      "field": "specializes",
      "target": "X7HYEBA5SA"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/YHZ9BCNDRZ.md",
  "msc": [
    "65M06",
    "35L65"
  ],
  "name": "Lax–Wendroff method",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/YHZ/YHZ9BCNDRZ.md",
  "status": null,
  "tag": "YHZ9BCNDRZ",
  "uri": "m2://YHZ9BCNDRZ",
  "url": "https://tamnd.github.io/math2/wiki/lax-wendroff-method/",
  "writing": {
    "tag": "YHZ9BCNDRZ",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}