A new implicit numerical method for the space and time fractional Bloch-Torrey equation


Autoria(s): Song, J.; Yu, Q.; Liu, F.; Turner, I.
Contribuinte(s)

Cheng, Wen

Sun, HongGuang

Baleanu, Dumitru

Data(s)

2012

Resumo

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

Identificador

http://eprints.qut.edu.au/51444/

Publicador

Hohai University

Relação

http://em.hhu.edu.cn/fda12/

Song, J., Yu, Q., Liu, F., & Turner, I. (2012) A new implicit numerical method for the space and time fractional Bloch-Torrey equation. In Cheng, Wen, Sun, HongGuang, & Baleanu, Dumitru (Eds.) Proceedings of the 5th Symposium on Fractional Differentiation and Its Applications, Hohai University, Hohai University, Nanjing, pp. 1-9.

Direitos

Copyright 2012 [please consult the author]

Fonte

School of Mathematical Sciences; Science & Engineering Faculty

Palavras-Chave #010000 MATHEMATICAL SCIENCES #Fractional Bloch-Torrey Equation #fractional calculus #implicit numerical method #fractional centered difference #stability #convergence
Tipo

Conference Paper