A Galerkin Finite Element Method to Solve Fractional Diffusion and Fractional Diffusion-Wave Equations
Küçük Resim Yok
Tarih
2013
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Vilnius Gediminas Tech Univ
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L2 and L1 are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.
Açıklama
Anahtar Kelimeler
finite element method, Galerkin method, fractional diffusion equation, fractional diffusion-wave equation, quadratic B-spline
Kaynak
Mathematical Modelling and Analysis
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
18
Sayı
2
