A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term
Year: 2019
Author: Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu, Xi-Le Zhao
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 4 : pp. 723–754
Abstract
Two implicit finite difference schemes combined with the Alikhanov's $L$2-1$σ$-formula are applied to one- and two-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability and $L$2-convergence of the methods are established. It is shown that the convergence order of the methods is equal to 2 both in time and space. Numerical experiments confirm the theoretical results. Moreover, since the arising linear systems can be ill-conditioned, three preconditioned iterative methods are employed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.200618.250319
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 4 : pp. 723–754
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Caputo fractional derivative L2-1σ-formula finite difference scheme time fractional reaction-diffusion equation iterative method.