SOLVING FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS BY PETROV-GALERKIN FINITE ELEMENT METHOD
Küçük Resim Yok
Tarih
2014
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Turkic World Mathematical Soc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In the last few years, it has become highly evident that fractional calculus has been widely used in several areas of science. Because of this fact, their numerical solutions also have become urgently important. In this manuscript, numerical solutions of both the fractional diffusion and fractional diffusion-wave equations have been obtained by a Petrov-Galerkin finite element method using quadratic B-spline base functions as trial functions and linear B-spline base functions as the test functions. In those equations, fractional derivatives are used in terms of the Caputo sense. While the L1 discretizaton formula has been applied to fractional diffusion equation, the L2 discretizaton formula has been applied to the fractional diffusion-wave equation. Finally, the error norms L-2 and L-infinity have been calculated for testing the accuracy of the proposed scheme.
Açıklama
Anahtar Kelimeler
Finite element method, Petrov-Galerkin method, Fractional diffusion equation, Fractional diffusion-wave equation, Quadratic B-Spline, Linear B-Spline
Kaynak
Twms Journal of Applied and Engineering Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
4
Sayı
2
