Volume 9, Issue 4
A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

Yong-Liang Zhao ,  Pei-Yong Zhu ,  Xian-Ming Gu and Xi-Le Zhao


East Asian J. Appl. Math., 9 (2019), pp. 723-754.

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  • Abstract

Two implicit finite difference schemes combined with the Alikhanov’s L2-1σformula are applied to one- and two-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability and L2 - 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.

  • History

Published online: 2019-10

  • AMS Subject Headings

65M06, 65M12, 65N06

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