TY - JOUR
T1 - Numerical Investigation of the Three-Dimensional Time-Fractional Extended Fisher-Kolmogorov Equation via a Meshless Method
AU - Liu , Jiaqi
AU - Ji , Cui-Cui
JO - Journal of Mathematical Study
VL - 4
SP - 460
EP - 475
PY - 2024
DA - 2024/12
SN - 57
DO - http://doi.org/10.4208/jms.v57n4.24.04
UR - https://global-sci.org/intro/article_detail/jms/23712.html
KW - Generalized finite difference method, meshless technique, TF-EFK equation, fourth-order nonlinear system, arbitrary domain.
AB - <p style="text-align: justify;">In this paper, we develop an efficient meshless technique for solving numerical solutions of the three-dimensional time-fractional extended Fisher-Kolmogorov
(TF-EFK) equation. Firstly, the $L2-1_σ$ formula on a general mesh is used to discretize
the Caputo fractional derivative, and then a weighted average technique at two neighboring time levels is adopted to implement the time discretization of the TF-EFK equation. After applying this time discretization, the generalized finite difference method
(GFDM) is introduced for the space discretization to solve the fourth-order nonlinear
algebra system generated from the TF-EFK equation with an arbitrary domain. Numerical examples are investigated to validate the performance of the proposed meshless GFDM in solving the TF-EFK equation in high dimensions with complex domains.</p>