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

Abstract

In this paper, we develop an efficient meshless technique for solving numer-ical 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 neigh-boring time levels is adopted to implement the time discretization of the TF-EFK equa-tion. 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. Nu-merical examples are investigated to validate the performance of the proposed mesh-less GFDM in solving the TF-EFK equation in high dimensions with complex domains.

Keywords

Generalized finite difference method / meshless technique / TF-EFK equation / fourth-order nonlinear system / arbitrary domain