Pith Number

pith:REFYVVI5

pith:2026:REFYVVI544VUVZ5F5UPPKSIINB

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Improving the local solution of the DG predictor of the ADER-DG method for solving systems of ordinary differential equations and its applicability to systems of differential-algebraic equations

I.S. Popov

Improved local solution for ADER-DG achieves one higher convergence order and continuity at grid nodes.

arxiv:2601.13908 v2 · 2026-01-20 · math.NA · cs.NA · math.FA · physics.app-ph · physics.comp-ph

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Claims

C1strongest claim

The improved local numerical solution demonstrates convergence orders of one higher than the convergence order of the local numerical solution of the original ADER-DG numerical method and has the property of continuity at grid nodes.

C2weakest assumption

The ε-embedding argument for DAE applicability assumes that the embedded ODE system inherits the stability and approximation properties of the original ADER-DG predictor without introducing new singularities or order reductions.

C3one line summary

An improved local solution for the ADER-DG DG predictor converges one order higher than the original, is continuous at nodes, and applies to DAEs with rigorous proofs.

References

89 extracted · 89 resolved · 1 Pith anchors

[1] Wiley, United Kingdom (2016) 2016

[2] Springer, Berlin, Heidelberg (1993) 1993

[3] Springer, Berlin, Heidelberg (1996) 1996

[4] Clarendon Press, Oxford (2001) 2001

[5] Springer, Verlag Berlin Heidelberg (1995) 1995

Receipt and verification

First computed	2026-05-26T01:03:22.691243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

890b8ad51de72b4ae7a5ed1ef54908686a0ef203e341e8751849fbaebbb3e76e

Aliases

arxiv: 2601.13908 · arxiv_version: 2601.13908v2 · doi: 10.48550/arxiv.2601.13908 · pith_short_12: REFYVVI544VU · pith_short_16: REFYVVI544VUVZ5F · pith_short_8: REFYVVI5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/REFYVVI544VUVZ5F5UPPKSIINB \
  | 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: 890b8ad51de72b4ae7a5ed1ef54908686a0ef203e341e8751849fbaebbb3e76e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e90b5a1ab84b6eaf2c3b36b49f235faf88c1d4fd3de71d63ba293ab7a94d53d",
    "cross_cats_sorted": [
      "cs.NA",
      "math.FA",
      "physics.app-ph",
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-01-20T12:34:49Z",
    "title_canon_sha256": "41b8a70be4b70f4c5454fe327ee696449ce9b132983c8531577e67f30657f73f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.13908",
    "kind": "arxiv",
    "version": 2
  }
}