Paper Citation Record · LEDGER

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations

As of 17 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2506.10820.

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

pith.paper-citation-record.v1
2506.10820 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:27:36.221874Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

31 of 31 outbound references displayed

verified exact2
verified fuzzy28
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b8b3efe4-51ce-40e4-bf6e-a7722763f6d8 · outbound

This paper cites 50 years of time parallel time integration,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations 50 years of time parallel time integration,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.861348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 643f45cf-943a-4b3d-81f1-bacf80c673c3 · outbound

This paper cites Applications of time parallelization,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Applications of time parallelization,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.844668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 03baf5de-22f0-4cbb-a6ad-2fc550169e39 · outbound

This paper cites A parareal in time discretization of PDEs,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations A parareal in time discretization of PDEs,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.826098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 48f33335-e18d-4d71-86e7-5d6de5f62186 · outbound

This paper cites Stable parareal in time method for first- and second- order hyperbolic systems,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Stable parareal in time method for first- and second- order hyperbolic systems,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.810081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 118d7e39-f4c1-4fb7-9576-e61d43eb3d29 · outbound

This paper cites A hybrid parareal spectral deferred corrections method,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations A hybrid parareal spectral deferred corrections method,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.792991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5b69fb26-3faa-40f2-8eae-f4e8391e3d25 · outbound

This paper cites On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.775492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8d9c9a75-8869-4e3a-9378-c8325c1c3beb · outbound

This paper cites Stability of the Parareal Algorithm,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Stability of the Parareal Algorithm,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.758237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 43a47aed-cffa-4c2f-8ae5-64f6032cb6cf · outbound

This paper cites Toward parallel coarse grid correction for parareal algorithm,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Toward parallel coarse grid correction for parareal algorithm,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.739035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b7825025-d034-4d3b-9cba-4fc2f23df113 · outbound

This paper cites A nonlinear paraexp algorithm.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations A nonlinear paraexp algorithm

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.723035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 162ed467-a54e-435f-b027-f87fc0934176 · outbound

This paper cites Optimal Schwarz waveform relax- ation for the one-dimensional wave equation,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Optimal Schwarz waveform relax- ation for the one-dimensional wave equation,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.707048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation fed1a40b-2414-434b-b5d8-b8a8978c2c01 · outbound

This paper cites The parareal in time iterative solver: A further direction to parallel implementation,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations The parareal in time iterative solver: A further direction to parallel implementation,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.686947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c07902b5-33e3-40c1-8d97-6cacd3f783fa · outbound

This paper cites Time spectral method for periodic and quasi-periodic unsteady computations on unstructured meshes,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Time spectral method for periodic and quasi-periodic unsteady computations on unstructured meshes,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.668138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6ae68d16-a000-4f92-8d79-4151eab563a3 · outbound

This paper cites Towards ef- ficient parallel-in-time simulation of periodic flows,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Towards ef- ficient parallel-in-time simulation of periodic flows,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.647115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4e276600-2ea5-4e6d-8d81-bfe71547b763 · outbound

This paper cites Parabolic multigrid methods,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Parabolic multigrid methods,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.483221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 522477bf-f206-492f-a7df-a93e3dd184d1 · outbound

This paper cites Analysis of a new space-time parallel multigrid algorithm for parabolic problems,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Analysis of a new space-time parallel multigrid algorithm for parabolic problems,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.298859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8d21204d-3ff6-42bd-84a6-d7a294fd439d · outbound

This paper cites Parallelization in time through tensor- product space–time solvers,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Parallelization in time through tensor- product space–time solvers,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:39.048442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 755051ee-d6eb-4349-b31b-167a85bb2db6 · outbound

This paper cites Preconditioning and iterative solution of all-at-once systems for evolutionary partial differential equa- tions,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Preconditioning and iterative solution of all-at-once systems for evolutionary partial differential equa- tions,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:38.861720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 403805bd-4d01-46e5-9132-a863bb412c75 · outbound

This paper cites Time parallelization for nonlinear problems based on diagonalization,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Time parallelization for nonlinear problems based on diagonalization,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:38.641409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8831922b-cc5e-457b-a60a-b9f0de03be86 · outbound

This paper cites Space-Time Methods: Fast Solvers and Applications,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Space-Time Methods: Fast Solvers and Applications,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:38.460528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9ec8f581-645a-48d3-a51b-69ed57c6d665 · outbound

This paper cites Multigrid methods with space–time concurrency,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Multigrid methods with space–time concurrency,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:38.238871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f3578af0-d0a9-445d-af8e-f76d4fd90bd3 · outbound

This paper cites Analysis of the parareal time-parallel time- integration method,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Analysis of the parareal time-parallel time- integration method,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:38.051025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6f100bd0-84b0-4990-8a2f-2e64b339da73 · outbound

This paper cites Convergence analysis of the Parareal-Euler algorithm for sys- tems of ODEs with complex eigenvalues,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Convergence analysis of the Parareal-Euler algorithm for sys- tems of ODEs with complex eigenvalues,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:37.879369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4f360dcc-1875-476b-b095-4e8bccdf403f · outbound

This paper cites A space-time multigrid method for parabolic partial differential equations,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations A space-time multigrid method for parabolic partial differential equations,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:37.736961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation cf2df5d4-ba7c-41c7-9011-459c02de6cc6 · outbound

This paper cites Parallel time integration with multigrid,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Parallel time integration with multigrid,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:37.593126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d31711ed-80c8-4ca4-95a6-f07f7e278c6a · outbound

This paper cites ParaDiag: parallel-in-time algorithms based on the diagonalization technique.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations ParaDiag: parallel-in-time algorithms based on the diagonalization technique

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T04:27:35.653166Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1112b05-f804-4578-b437-69575bf91de4 · outbound

This paper cites Towards developing robust algorithms for solv- ing partial differential equations on MIMD machines,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Towards developing robust algorithms for solv- ing partial differential equations on MIMD machines,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:37.421227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7593099c-29a9-4540-941a-2d6933755473 · outbound

This paper cites A time-stepping algorithm for parallel computers,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations A time-stepping algorithm for parallel computers,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:37.271899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 294091a2-12aa-4360-bfe2-71e58b9faf88 · outbound

This paper cites A rigorous analysis of time domain parallelism,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations A rigorous analysis of time domain parallelism,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:37.086309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 792e7598-05bd-48f6-9fb2-73392535c771 · outbound

This paper cites A New Parallel-in-time Direct Inverse Method for Nonlinear Differential Equations.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations A New Parallel-in-time Direct Inverse Method for Nonlinear Differential Equations

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:27:36.726974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 3927dafd-7e9d-4f5b-9dc4-1bb65cb8a311 · outbound

This paper cites Convergence of Parareal with spatial coarsening,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Convergence of Parareal with spatial coarsening,

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:27:36.920745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 257fded3-a3bc-4dca-81c5-a91ce88d29e9 · outbound

This paper cites Impact of spatial coarsening on Parareal convergence,.

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations Impact of spatial coarsening on Parareal convergence,

Reference 31

Resolution: verified exact; raw_fallback, observed 2026-08-07T04:27:36.594352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.