Volume 12, Issue 4
A Linearized Second-Order Difference Scheme for the Nonlinear Time-Fractional Fourth-Order Reaction-Diffusion Equation

Hong Sun ,  Zhi-zhong Sun and Rui Du


Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 1168-1190.

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  • Abstract

This paper presents a second-order linearized finite difference scheme for the nonlinear time-fractional fourth-order reaction-diffusion equation. The temporal Caputo derivative is approximated by $L2$-$1_\sigma$ formula with the approximation order of $\mathcal{O}(\tau^{3-\alpha}).$ The unconditional stability and convergence of the proposed scheme are proved by the discrete energy method. The scheme can achieve the global second-order numerical accuracy both in space and time. Three numerical examples are given to verify the numerical accuracy and efficiency of the difference scheme.

  • History

Published online: 2019-06

  • AMS Subject Headings

65M06, 65M12, 65M15

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