TY - JOUR
T1 - Higher-Order Linearized Multistep Finite Difference Methods for Non-Fickian Delay Reaction-Diffusion Equations
AU - Q.-F. Zhang, M. Mei & C.-J. Zhang
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 1
EP - 19
PY - 2016
DA - 2016/01
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/407.html
KW - Non-Fickian delay reaction-diffusion equation, linearized compact/noncompact, multistep finite difference scheme, solvability, convergence.
AB - <p style="text-align: justify;">In this paper, two types of higher-order linearized multistep finite difference schemes
are proposed to solve non-Fickian delay reaction-diffusion equations. For the first scheme, the
equations are discretized based on the backward differentiation formulas in time and compact finite
difference approximations in space. The global convergence of the scheme is proved rigorously with
convergence order $\mathcal{O}(\tau^2 + h^4)$ in the maximum norm. Next, a linearized noncompact multistep
finite difference scheme is presented and the corresponding error estimate is established. Finally,
extensive numerical examples are carried out to demonstrate the accuracy and efficiency of the
schemes, and some comparisons with the implicit Euler scheme in the literature are presented to
show the effectiveness of our schemes.</p>