Simulation of linear and nonlinear advection–diffusion–reaction problems by a novel localized scheme

Abstract

This paper presents a new meshless scheme based on the compactly supported radial basis functions for solving linear and nonlinear advection–diffusion–reaction equations. The simulation of proposed problems is divided into the rough approximation obtained from the boundary conditions and corrected approximation using compactly supported radial basis functions where a sparse system matrix will be obtained. The behaviors of the method are verified by several examples which indicate its accuracy and efficiency.