Paper Info
Title
Numerical simulation of the fractional Bloch equations.
Abstract
In physics and chemistry, specifically in NMR (nuclear magnetic resonance) or MRI (magnetic resonance imaging), or ESR (electron spin resonance) the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = ( M x , M y , M z ) as a function of time when relaxation times T 1 and T 2 are present. Recently, some fractional models have been proposed for the Bloch equations, however, effective numerical methods and supporting error analyses for the fractional Bloch equation (FBE) are still limited.In this paper, the time-fractional Bloch equations (TFBE) and the anomalous fractional Bloch equations (AFBE) are considered. Firstly, we derive an analytical solution for the TFBE with an initial condition. Secondly, we propose an effective predictor-corrector method (PCM) for the TFBE, and the error analysis for PCM is investigated. Furthermore, we derive an effective implicit numerical method (INM) for the anomalous fractional Bloch equations (AFBE), and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the AFBE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.
Year
DOI
Venue
2014
10.1016/j.cam.2013.06.027
J. Computational Applied Mathematics
Keywords
Field
DocType
Time fractional Bloch equations,Anomalous fractional Bloch equations,Implicit numerical method,Predictor–corrector method,Stability,Convergence
Convergence (routing),Bloch wave,Bloch equations,Computer simulation,Mathematical analysis,Magnetization,Mathematical physics,Initial value problem,Numerical analysis,Predictor–corrector method,Mathematics
Journal
Volume
Issue
ISSN
255
C
0377-0427
Citations 
PageRank 
References 
7
0.69
5
Authors
4
Name
Order
Citations
PageRank
Q. Yu1453.73
F. Liu238840.96
Ian Turner31016122.29
K. Burrage423636.73