Superconvergent Meshless Collocation Method for Nonlinear Neutral Delay‐Reaction‐Diffusion Equation

ABSTRACT In this article, a novel meshless superconvergent finite point method (SFPM) is developed for a class of nonlinear neutral delay‐reaction‐diffusion (NDRD) equation. We begin with a second‐order scheme to obtain the temporal semi‐discretization of the nonlinear NDRD equation. Then, in order to enhance accuracy and superconvergence, we adopt the stabilized moving least squares approximation and its smoothed derivatives to present the numerical solution, and the eventual discrete algebraic system is established by employing the collocation technology. Moreover, the theoretical accuracy of the SFPM for solving nonlinear NDRD problem in ‐dimensional space is established. Numerical simulations validate the effectiveness and superconvergence of the SFPM.