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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.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v57n4.24.04}, url = {http://global-sci.org/intro/article_detail/jms/23712.html} }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.