East Asian J. Appl. Math., 9 (2019), pp. 723-754.
Published online: 2019-10
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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} }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.