@Article{NMTMA-12-4,
author = {Rui, Du and Sun, Hong and Zhi-Zhong, Sun and Rui, Du},
title = {A Linearized Second-Order Difference Scheme for the Nonlinear Time-Fractional Fourth-Order Reaction-Diffusion Equation},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2019},
volume = {12},
number = {4},
pages = {1168--1190},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2017-0144},
url = {https://global-sci.com/article/90435/a-linearized-second-order-difference-scheme-for-the-nonlinear-time-fractional-fourth-order-reaction-diffusion-equation}
}