Collocation Finite Element Method for the Fractional Fokker-Planck Equation
Küçük Resim Yok
Tarih
2025
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Wiley
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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 L2$$ {L}_2 $$ and L infinity$$ {L}_{\infty } $$ 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. This study explores approximate solutions for fractional Fokker-Planck equations using general finite element schemes developed via the collocation finite element method with trigonometric quintic B-spline basis functions. It validates these methods on two fundamental problems and compares numerical results, including L2$$ {L}_2 $$ and L infinity$$ {L}_{\infty } $$ error norms across different temporal and spatial steps, against exact solutions and alternative methods. The findings highlight strong agreement between approximate and exact solutions, particularly when employing higher numbers of spatial and temporal elements. image
Açıklama
Anahtar Kelimeler
collocation finite element method, fractional Fokker-Planck equation, trigonometric quintic B-spline
Kaynak
International Journal For Numerical Methods in Fluids
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
97
Sayı
3
