Collocation Finite Element Method for the Fractional Fokker–Planck Equation

Karabenli H., ESEN A., UÇAR Y.

International Journal for Numerical Methods in Fluids, vol.97, no.3, pp.224-232, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 97 Issue: 3
  • Publication Date: 2025
  • Doi Number: 10.1002/fld.5343
  • Journal Name: International Journal for Numerical Methods in Fluids
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.224-232
  • Keywords: collocation finite element method, fractional Fokker–Planck equation, trigonometric quintic B-spline
  • Inonu University Affiliated: Yes

Abstract

In this study, the approximate results of the fractional Fokker–Planck equations have been investigated. First, finite element schemes have been obtained using collocation finite element method based on the trigonometric quintic B-spline basis functions. Then, the present method is tested on two fundamental problems having appropriate initial conditions. The newly obtained numerical results contained the error norms (Formula presented.) and (Formula presented.) for various temporal and spatial steps are compared with the exact ones and other solutions. More accurate results have been obtained for large numbers of spatial and temporal elements.