Finite difference methods and a fourier analysis for the fractional reaction–subdiffusion equation
Chen, Chang-ming, Liu, Fawang, & Burrage, Kevin (2008) Finite difference methods and a fourier analysis for the fractional reaction–subdiffusion equation. Applied Mathematics and Computation, 198(2), pp. 754-769.
Various fields of science and engineering deal with dynamical systems that can be described by fractional partial differential equations (FPDE), for example, systems biology, chemistry and biochemistry applications due to anomalous diffusion effects in constrained environments. However, effective numerical methods and numerical analysis for FPDE are still in their infancy. In this paper, we consider a fractional reaction–subdiffusion equation (FR-subDE) in which both the motion and the reaction terms are affected by the subdiffusive character of the process. Using the relationship between the Riemann–Liouville and Grünwald–Letnikov definitions of fractional derivatives, an implicit and an explicit difference methods for the FR-subDE are presented. The stability and the convergence of the two numerical methods are investigated by a Fourier analysis. The solvability of the implicit finite difference method is also proved. The high-accuracy algorithm is structured using Richardson extrapolation. Finally, a comparison between the exact solution and the two numerical solutions is given. The numerical results are in excellent agreement with our theoretical analysis.
Impact and interest:
Citation counts are sourced monthly from and 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 theindexing service can be viewed at the linked Google Scholar™ search.
Full-text downloads displays 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.
Repository Staff Only: item control page