SOLVING FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS BY PETROV-GALERKIN FINITE ELEMENT METHOD

A. ESEN; Y. UUCAR; M. YAGMURLU; O. TASBOZAN

Makale detayları

SOLVING FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS BY PETROV-GALERKIN FINITE ELEMENT METHOD

Yazarlar:

A. ESEN | Y. UUCAR | M. YAGMURLU | O. TASBOZAN

Yayıncı:

Turkic World Mathematical Society

Dergi:

TWMS Journal of Applied and Engineering Mathematics 2014 Vol.4 Issue 2, pp.155-168

Belge Tipi:

Makale

Yayın Tarihi:

11/2014

Belge Dili:

İngilizce

Document ID (Org No.):

2000746252

Sıklık:

Aylık

eISSN:

2587-1013

pISSN:

2146-1147

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.

Makale detayları

SOLVING FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS BY PETROV-GALERKIN FINITE ELEMENT METHOD

Yazarlar: A. ESEN | Y. UUCAR | M. YAGMURLU | O. TASBOZAN

Yayıncı: Turkic World Mathematical Society

Dergi: TWMS Journal of Applied and Engineering Mathematics 2014 Vol.4 Issue 2, pp.155-168

Belge Tipi: Makale

Yayın Tarihi: 11/2014

Belge Dili: İngilizce

Document ID (Org No.): 2000746252

Sıklık: Aylık

eISSN: 2587-1013

pISSN: 2146-1147

Sayı

Yazarlar:

A. ESEN | Y. UUCAR | M. YAGMURLU | O. TASBOZAN

Yayıncı:

Turkic World Mathematical Society

Dergi:

TWMS Journal of Applied and Engineering Mathematics 2014 Vol.4 Issue 2, pp.155-168

Belge Tipi:

Makale

Yayın Tarihi:

11/2014

Belge Dili:

İngilizce

Document ID (Org No.):

2000746252

Sıklık:

Aylık

eISSN:

2587-1013

pISSN:

2146-1147