Pith Number

pith:VO2A5OBD

pith:2026:VO2A5OBDTYFOJIV4PJXUVCXMIV

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Nonlinear numerical schemes using specular differentiation for initial value problems of first-order ordinary differential equations

Kiyuob Jung

Specular differentiation defines nonlinear numerical schemes for first-order ODE initial value problems with proven second-order accuracy and exact integration along ellipses.

arxiv:2601.09900 v4 · 2026-01-14 · math.NA · cs.NA

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We select one scheme and prove its second-order consistency and convergence. By modifying this scheme, we also obtain a numerical scheme with zero local truncation error for ODEs whose solution trajectories are ellipses.

C2weakest assumption

The quasi-Fermat theorem and quasi-Mean Value Theorem hold for the newly defined specular differentiation operator and can be used to derive the truncation error bounds without additional restrictions on the solution.

C3one line summary

Introduces specular differentiation to create second-order consistent numerical schemes for ODE IVPs, including a modified version with zero local truncation error on elliptical trajectories.

Receipt and verification

First computed	2026-06-09T01:05:12.761287Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abb40eb8239e0ae4a2bc7a6f4a8aec454c4974d3d55402e986657153697ed347

Aliases

arxiv: 2601.09900 · arxiv_version: 2601.09900v4 · doi: 10.48550/arxiv.2601.09900 · pith_short_12: VO2A5OBDTYFO · pith_short_16: VO2A5OBDTYFOJIV4 · pith_short_8: VO2A5OBD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VO2A5OBDTYFOJIV4PJXUVCXMIV \
  | 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: abb40eb8239e0ae4a2bc7a6f4a8aec454c4974d3d55402e986657153697ed347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86c518c7dc52b967d014bf9781fa7581e6b41f4422210b0e6cfd61f83f06b0d6",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-01-14T22:14:24Z",
    "title_canon_sha256": "a70d7e07d89aaf4e7ef5fa0858856791132a3d23e30afccf42ccb18712544b89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.09900",
    "kind": "arxiv",
    "version": 4
  }
}