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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.