A Local RBF‐Based Differential Quadrature Method for Solving the Gray–Scott Model

ABSTRACT By using the local Radial Basis Function‐based Differential Quadrature method (LRBF‐DQ), a numerical simulation technique for Gray–Scott Reaction‐Diffusion (RD) systems was proposed. This paper has used the LRBF‐DQ method for space discretization with Crank–Nicolson format combined with nonlinear processing for time discretization to obtain the numerical format. In addition, the stability of this format was also analyzed by plotting the eigenvalue of the iteration matrix, and an unconditionally stable result was obtained. The LRBF‐DQ method combined with nonlinear processing was used for the first time to simulate the 2D Gray–Scott RD system in this article. After numerical testing, it was found that under the same conditions, this method has higher accuracy and can simulate better spot images with fewer points and longer time intervals.