Journals
Resources
About Us
Open Access

Numerical Investigation of the Three-Dimensional Time-Fractional Extended Fisher-Kolmogorov Equation via a Meshless Method

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Jiaqi Liu

Cui-Cui Ji