Paper Citation Record · LEDGER

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition

As of 16 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:1908.07403.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.07403 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T12:26:51.019497Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

29 of 29 outbound references displayed

verified exact0
verified fuzzy16
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8c066f7d-f8b9-49f8-b024-8ae87b6295a6 · outbound

This paper cites Hustedt, S.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Hustedt, S

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:52.387037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f0108be1-f76e-430d-b6fb-f778153e2376 · outbound

This paper cites Wu, A dispersion minimizing compact ﬁnite difference scheme for the 2d helmholtz equation, Journal of Com- putational and Applied Mathematics 311 (2017) 497–512.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Wu, A dispersion minimizing compact ﬁnite difference scheme for the 2d helmholtz equation, Journal of Com- putational and Applied Mathematics 311 (2017) 497–512

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:52.344177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1225b2fd-017f-4935-a2f7-84d9750f16e4 · outbound

This paper cites Ihlenburg, I.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Ihlenburg, I

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:52.297867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6f3117d7-8c73-4385-9442-cf30177d8379 · outbound

This paper cites Ihlenburg, I.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Ihlenburg, I

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:52.223856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0b3132c4-a2b0-43e2-91dd-4587d66456a2 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:52.142938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d2679049-c7d0-4d51-b0fd-a0a0eef07313 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:52.097100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e77d6474-97fc-4830-9b2b-74a78533a8b8 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:52.063716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 35d20eb8-eede-451b-8335-9f6901d67155 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:52.007616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e67de963-56e6-4e78-8471-ee05e446d557 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.960708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 553141b9-a5ab-4109-8b9b-1b10a3b7bcca · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.916660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 97da485d-9747-4fca-a4e5-4fe086e4d45a · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.880371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e2719e3c-e38e-4e88-8922-87038b3cdf04 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.835016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6fa81d92-f8d7-44b2-b3f1-d12d398cdebb · outbound

This paper cites Chen, A generalized optimal 9-point scheme for fr equency-domain scalar wave equation, Journal of Applied Geophysics 92 (2013) 1–7.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Chen, A generalized optimal 9-point scheme for fr equency-domain scalar wave equation, Journal of Applied Geophysics 92 (2013) 1–7

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.794063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 23165e2f-824d-4e23-b6df-23930e4c3b87 · outbound

This paper cites Collino, P.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Collino, P

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.741449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation eef4aa62-facd-41ba-8f11-eee7ced79343 · outbound

This paper cites Berenger, A perfectly matched layer for the absor ption of electromagnetic waves, Journal of computational physics 114 (2) (1994) 185–200.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Berenger, A perfectly matched layer for the absor ption of electromagnetic waves, Journal of computational physics 114 (2) (1994) 185–200

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.701286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 02913e62-a530-482e-a019-912c19f1022f · outbound

This paper cites Turkel, A.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Turkel, A

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.627078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 14491722-3b3f-4d34-8259-6de313a47413 · outbound

This paper cites Singer, E.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Singer, E

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.591034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8d10f3fb-93ba-4b6a-a64b-d711fed4538b · outbound

This paper cites Cheng, X.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Cheng, X

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.560289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ee900fcf-1f6a-4bb3-868e-734e3b778fd5 · outbound

This paper cites Harari, E.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Harari, E

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.512455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 69c08b75-cfce-4b7a-b895-349d76624baf · outbound

This paper cites Singer, E.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Singer, E

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.476318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7c8a61bd-75dd-4b9b-b32a-0782c8c21fbc · outbound

This paper cites Britt, S.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Britt, S

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.440422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8bb368b4-0b56-4398-a4c1-8706c27133d5 · outbound

This paper cites Sutmann, Compact ﬁnite difference schemes of sixth o rder for the helmholtz equation, Journal of Computational and Applied Mathematics 203 (1) (2007) 15–31.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Sutmann, Compact ﬁnite difference schemes of sixth o rder for the helmholtz equation, Journal of Computational and Applied Mathematics 203 (1) (2007) 15–31

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.402527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4ba62606-16ed-4111-8690-805e4f19746b · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.366512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2f7dbe86-d1cb-4215-b4f9-54a5a4825711 · outbound

This paper cites Turkel, D.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Turkel, D

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.327511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e57a3e0e-c235-49e3-9777-c1106be8b1d2 · outbound

This paper cites Dastour, W.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Dastour, W

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:26:51.289444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 708db289-6ee3-49c4-a04d-c7dbfdd2ed07 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.248952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 65ea86dc-e1bf-46c7-89f5-2d375f275fe4 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.199411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9aad3463-1e1e-46bb-848c-18037098182a · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.163899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2dcfab1f-98d4-4a6f-92e8-fabbf4d86ac3 · outbound

This paper cites an unresolved cited work.

A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:26:51.124613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

No inbound Pith citation observations are available.