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The authors acknowledge the support of the Escuela Tecnica Superior de Ingenieros Industriales (UNED) of Spain, project 2019-IFC02, and of the Universidad Politecnica de Madrid (UPM) (Research groups 2019).

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Gavete, LuisAuthorBenito, Juan JoséAuthor

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December 24, 2019
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Non-linear Fokker-Planck equation solved with generalized finite differences in 2D and 3D

Publicated to:Applied Mathematics And Computation. 368 (UNSP 124801): - 2020-01-01 368(UNSP 124801), DOI: 10.1016/j.amc.2019.124801

Authors: Urena, Francisco; Gavete, Luis; Garcia Gomez, Angel; Jose Benito, Juan; Manuel Vargas, Antonio;

Affiliations

Ingeniería Sísmica: Dinámica de Suelos y Estructuras. Universidad Politécnica de Madrid - Author
UCM, Madrid, Spain - Author
UNED, ETSII, Madrid, Spain - Author
UPM, ETSIE, Madrid, Spain - Author

Abstract

The generalized finite difference method (GFDM) has been proved to be a good meshless method to solve several both linear and nonlinear partial differential equations (PDEs): wave propagation, advection-diffusion, plates, beams, etc. In this paper it is shown the application of the GFDM for solving the linear and nonlinear Fokker-Planck equation in 2D and 3D. Criteria for convergence of fully explicit method using GFDM for Fokker-Planck equation in 2D and 3D are given. Published by Elsevier Inc.

Keywords

Advection - diffusionExplicit methodFinite difference methodFokker planck equationFokker-planck equationGeneralized finite differenceGeneralized finite difference methodGeneralized finite-difference methodMesh-less methodsMeshless methodsNon linearNonlinear equationsNonlinear fokker-planck equationsNonlinear partial differential equationsPartial differential equationsWave propagation

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Applied Mathematics And Computation due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2020, it was in position 7/265, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations from Scopus Elsevier, it yields a value for the Field-Weighted Citation Impact from the Scopus agency: 1.19, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Field Citation Ratio (FCR) from Dimensions: 7.93 (source consulted: Dimensions Jul 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-07-15, the following number of citations:

  • WoS: 4
  • Scopus: 16

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-15:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 13 (PlumX).