TY - JOUR
T1 - A Linearized Second-Order Difference Scheme for the Nonlinear Time-Fractional Fourth-Order Reaction-Diffusion Equation
AU - Sun , Hong
AU - Sun , Zhi-zhong
AU - Du , Rui
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1168
EP - 1190
PY - 2019
DA - 2019/06
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2017-0144
UR - https://global-sci.org/intro/article_detail/nmtma/13219.html
KW - Fractional differential equation,  Caputo derivative,   high order equation, nonlinear, linearized, difference scheme, convergence, stability.
AB - <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>