A Local RBF-Based Differential Quadrature Method for Solving the Time-Fractional Reaction–Diffusion Systems

By using the Local Radial Basis Function-based Differential Quadrature (LRBF-DQ) method, a numerical simulation technique for the time-fractional Reaction–Diffusion (RD) systems in regular and irregular regions was proposed. In this paper, the LRBF-DQ method combined with the L1-2 formula to approximate the Caputo fractional derivative of order [Formula: see text] is used for the first time, and Neumann boundary conditions are treated by the Finite Difference Method (FDM). Through numerical tests, the method has higher accuracy, and can provide accurate numerical solutions and image simulations of the time-fractional RD systems. As the same time, when [Formula: see text], as the [Formula: see text] value becomes smaller, the time required for the pattern simulated by the system becomes longer. This provides a new meshless method for studying the formation of stable solutions in the time-fractional RD systems, which can handle the system accurately and effectively.