Pith Number

pith:IBUWS3UX

pith:2025:IBUWS3UXKW7TCJH6RSZV6CVZE2

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An L-Stable Implicit Two-Stage Fourth-Order Temporal Discretization Scheme for Lax-Wendroff-Type Solvers Applied to Stiff Problems

Zhixin Huo

An implicit two-stage fourth-order scheme brings L-stability to Lax-Wendroff solvers for stiff problems.

arxiv:2512.01628 v4 · 2025-12-01 · math.NA · cs.NA

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Claims

C1strongest claim

Numerical experiments on classical stiff benchmarks show that the proposed implicit scheme achieves fourth-order temporal accuracy in two stages. Compared to the classical fourth-order implicit Runge-Kutta method, it allows larger stable time steps and reduces convergence errors by an order of magnitude.

C2weakest assumption

The L-stability conditions derived from a linear model equation via the maximum modulus principle extend to the nonlinear systems and coupled spatial discretizations in Lax-Wendroff-type solvers for stiff problems.

C3one line summary

An L-stable implicit two-stage fourth-order temporal discretization scheme is constructed for Lax-Wendroff-type solvers on stiff problems, achieving fourth-order accuracy with larger time steps than classical implicit Runge-Kutta methods.

Formal links

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Cited by

1 paper in Pith

Arbitrary-Order Pad\'e-Closed Anchored Two-Derivative Time Discretizations: $s$ Active Stages, Order $2s$, and $L$-Stability

Receipt and verification

First computed	2026-06-23T03:13:52.165245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4069696e9755bf3124fe8cb35f0ab9268011ed1c109ee92ae540637479ea3f78

Aliases

arxiv: 2512.01628 · arxiv_version: 2512.01628v4 · doi: 10.48550/arxiv.2512.01628 · pith_short_12: IBUWS3UXKW7T · pith_short_16: IBUWS3UXKW7TCJH6 · pith_short_8: IBUWS3UX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IBUWS3UXKW7TCJH6RSZV6CVZE2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4069696e9755bf3124fe8cb35f0ab9268011ed1c109ee92ae540637479ea3f78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "107c82adb91a75a209d2c0e768158ff2809b7f8d9695927fbde8c311f8325f8b",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-12-01T12:50:25Z",
    "title_canon_sha256": "547d1746945432435120cbf1b1c6b42ea87fe56f43f3d3a82faf264133bf7b69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.01628",
    "kind": "arxiv",
    "version": 4
  }
}