QUT ePrints

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

Zhuang, P., Liu, F., Anh, V., & Turner, I. W. (2009) Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process. IMA Journal of Applied Mathematics, 74(5), pp. 645-667.

View at publisher

Abstract

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP):

Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Impact and interest:

15 citations in Scopus
Search Google Scholar™
10 citations in Web of Science®

Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

152 since deposited on 18 Jan 2010
40 in the past twelve months

Full-text downloadsdisplays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 29759
Item Type: Journal Article
Additional URLs:
Keywords: fractional reaction–subdiffusion equation, implicit numerical method, convergence and stability, energy method
DOI: 10.1093/imamat/hxp015
ISSN: 0272-4960
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Deposited On: 19 Jan 2010 07:33
Last Modified: 01 Mar 2012 10:04

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page