Solving fractional diffusion and fractional diffusion-wave equations by Petrov-Galerkin finite element method
Künye
Esen, A., Uçar, Y., Yağmurlu, N. M. & Taşbozan, O. (2014). Solving fractional diffusion and fractional diffusion-wave equations by Petrov-Galerkin finite element method. TWMS Journal of Applied and Engineering Mathematics, 4(2), 155-168.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 L2 and L? have been calculated for testing the accuracy of the proposed scheme.
Cilt
4Sayı
2Bağlantı
http://belgelik.isikun.edu.tr/xmlui/handle/iubelgelik/2530http://jaem.isikun.edu.tr/web/index.php/archive/88-vol4no2/178
Koleksiyonlar
Aşağıdaki lisans dosyası bu öğe ile ilişkilidir: