Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T14:18:29.999186Z
Paper Citation Record · LEDGER
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform
As of 20 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2412.12308.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-12T03:23:42.788576Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-12T03:26:19.759557Z
Reference resolution
23 of 23 outbound references displayed
- verified exact4
- verified fuzzy13
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation d35159fb-2f2b-4318-b093-792606c91f53 · outbound
This paper cites an unresolved cited work.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:18:31.912988Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 975f32fe-50b7-44e3-a96c-7dbd336336e6 · outbound
This paper cites The second property allows us to recover the original function from its Fourier components via the inverse DFT (iDF T) given by: pj = 1 N N −1X k=0 Pkω−jk N , (10) 3 FIG.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform The second property allows us to recover the original function from its Fourier components via the inverse DFT (iDF T) given by: pj = 1 N N −1X k=0 Pkω−jk N , (10) 3 FIG
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:31.830693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8c537d6a-be23-464e-aa14-271fab364326 · outbound
This paper cites The problem is to solve the wave equation for an initial time-symmetric spherically symmetric Gaussian pulse in the domain D = [−1, 1]2.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform The problem is to solve the wave equation for an initial time-symmetric spherically symmetric Gaussian pulse in the domain D = [−1, 1]2
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:31.740512Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ce118d62-6637-42b7-9266-64f6d75450c1 · outbound
This paper cites an unresolved cited work.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:18:31.624668Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation bcf53d0a-9d26-46a8-8601-a47ab8efa8a4 · outbound
This paper cites Revisiting spherically symmetric relativistic hydrody- namics,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Revisiting spherically symmetric relativistic hydrody- namics,
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:31.109230Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 43e3b1eb-deb3-40c0-ae4a-8e56cae3d152 · outbound
This paper cites an unresolved cited work.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:18:31.488730Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5b252ad2-3428-446f-8c7d-fe772b373de6 · outbound
This paper cites Solving the time-dependent schroedinger equation using finite difference methods,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Solving the time-dependent schroedinger equation using finite difference methods,
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:31.391374Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9c7f7298-5578-4de7-8981-0864b2fd084b · outbound
This paper cites Soluci´ on de la ecuaci´ on de onda como un problema de valores iniciales usando diferencias finitas,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Soluci´ on de la ecuaci´ on de onda como un problema de valores iniciales usando diferencias finitas,
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:31.294507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f25c2358-9b12-4a7b-8497-eaec543d459e · outbound
This paper cites Pseudospectral vs finite differences methods in numer- ical relativity,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Pseudospectral vs finite differences methods in numer- ical relativity,
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:31.196082Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 905b7f16-1e50-4bc7-a73a-2e54a1cfdfaa · outbound
This paper cites an unresolved cited work.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:18:30.740848Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation aa5cc676-29e3-47c9-acc1-7caedceeb994 · outbound
This paper cites Exact solution of the 1d shock-tube problem in newtonian and relativistic hydrodynamics,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Exact solution of the 1d shock-tube problem in newtonian and relativistic hydrodynamics,
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:31.026141Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ff8a69f9-b55c-4843-81be-615c930f374d · outbound
This paper cites Spherical accretion of a perfect fluid onto a black hole,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Spherical accretion of a perfect fluid onto a black hole,
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:30.965162Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation eafdd352-f855-4c08-9d4a-41f40fe80e81 · outbound
This paper cites An algorithm for the machine calculation of complex fourier series,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform An algorithm for the machine calculation of complex fourier series,
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:30.911770Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a8a7ce98-2afd-4534-beeb-da77e8856d4f · outbound
This paper cites Spiegel, Schaum’s Outline of Fourier Analysis with Applications to Boundary Value Problems , Schaum’s Outline Series (McGraw Hill LLC, 1974).
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Spiegel, Schaum’s Outline of Fourier Analysis with Applications to Boundary Value Problems , Schaum’s Outline Series (McGraw Hill LLC, 1974)
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:30.836059Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c81c169b-0887-4b29-ac41-d62f74c6ed16 · outbound
This paper cites A Living Review of Quantum Computing for Plasma Physics.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform A Living Review of Quantum Computing for Plasma Physics
Reference 15
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T14:18:30.442026Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 352062d4-64c1-4c94-a1cb-b34d74b028c6 · outbound
This paper cites Galaxy Formation with BECDM: I. Turbulence and relaxation of idealised haloes.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Galaxy Formation with BECDM: I. Turbulence and relaxation of idealised haloes
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T14:18:29.708396Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4764c09d-c4a5-4178-acde-bcf54962ee73 · outbound
This paper cites Explo- ration of simple scenarios involving fuzzy dark matter cores and gas at local scales,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Explo- ration of simple scenarios involving fuzzy dark matter cores and gas at local scales,
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T14:18:29.754246Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d0231870-cfe7-4457-b210-5d6b012c4fa3 · outbound
This paper cites Mathematical theory and numerical methods for bose-einstein condensation,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Mathematical theory and numerical methods for bose-einstein condensation,
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:30.647788Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b2c2c0b6-919a-4250-adf5-a670ccb7f7f2 · outbound
This paper cites Variational quantum crank-nicolson and method-of- lines schemes for the solution of initial value problems,.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Variational quantum crank-nicolson and method-of- lines schemes for the solution of initial value problems,
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:30.575105Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8ae00f23-c629-4343-baa5-b0a5128d8c8d · outbound
This paper cites Application of a variational hybrid quantum-classical algorithm to heat conduction equation.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Application of a variational hybrid quantum-classical algorithm to heat conduction equation
Reference 21
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T14:18:30.364483Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 68eacebf-4f21-49dc-912e-161ae154a646 · outbound
This paper cites Variational Quantum Evolution Equation Solver.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Variational Quantum Evolution Equation Solver
Reference 22
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T14:18:30.276654Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 13fc93b6-3953-46ce-83b4-4427e2d19a70 · outbound
This paper cites Quantum Variational Solving of Nonlinear and Multi-Dimensional Partial Differential Equations.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Quantum Variational Solving of Nonlinear and Multi-Dimensional Partial Differential Equations
Reference 23
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T14:18:30.125553Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6375694e-3c73-44ca-b7c6-eeb1c7edf82f · outbound
This paper cites Vari- ous snapshots of the solution, obtained using the Runge- Kutta 4 (RK4) scheme to integrate Eq.
Numerical Solution Partial Differential Equations using the Discrete Fourier Transform Vari- ous snapshots of the solution, obtained using the Runge- Kutta 4 (RK4) scheme to integrate Eq
Reference 256
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:18:31.556787Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
Observation 0e133269-c7cd-4180-b59b-2a9142ec2589 · inbound
Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators cites this paper.
Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Numerical Solution Partial Differential Equations using the Discrete Fourier Transform
Reference 24
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T03:26:19.762212Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.