@Article{EAJAM-9-723, author = {Zhao , Yong-LiangZhu , Pei-YongGu , Xian-Ming and Zhao , Xi-Le}, title = {A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.200618.250319}, url = {http://global-sci.org/intro/article_detail/eajam/13330.html} }