TY - JOUR
T1 - A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term
AU - Zhao , Yong-Liang
AU - Zhu , Pei-Yong
AU - Gu , Xian-Ming
AU - Zhao , Xi-Le
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 723
EP - 754
PY - 2019
DA - 2019/10
SN - 9
DO - http://doi.org/10.4208/eajam.200618.250319
UR - https://global-sci.org/intro/article_detail/eajam/13330.html
KW - Caputo fractional derivative, L2-1σ-formula, finite difference scheme, time fractional
reaction-diffusion equation, iterative method.
AB - <p style="text-align: justify;">Two implicit finite difference schemes combined with the Alikhanov&#39;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.</p>