Numerical Investigation of the Three-Dimensional Time-Fractional Extended Fisher-Kolmogorov Equation via a Meshless Method
Year: 2024
Author: Jiaqi Liu, Cui-Cui Ji
Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 460–475
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v57n4.24.04
Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 460–475
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Generalized finite difference method meshless technique TF-EFK equation fourth-order nonlinear system arbitrary domain.