Numerical Investigation of the Three-Dimensional Time-Fractional Extended Fisher-Kolmogorov Equation via a Meshless Method (Journal of Mathematical Study, 2024)
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 discretizethe 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 nonlinearalgebra 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.