A Linearized Second-Order Difference Scheme for the Nonlinear Time-Fractional Fourth-Order Reaction-Diffusion Equation
Year: 2019
Author: Rui Du, Hong Sun, Zhi-Zhong Sun, Rui Du
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 4 : pp. 1168–1190
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2017-0144
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 4 : pp. 1168–1190
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Fractional differential equation Caputo derivative high order equation nonlinear linearized difference scheme convergence stability.
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