The coupled advection-dominated diffusion-reaction equations which arise in the prevention of groundwater contamination problem are approximated by the compact local integrated radial basis function (CLIRBF) method. To efficiently solve the resulting nonlinear system of advection-diffusion equations, we use the integrated radial basis function (IRBF) for discretizing the spatial variables. Afterwards, the system of ordinary differential equations (ODEs) obtained is discretized by the method of lines (MOL). MOL is a general way of viewing a partial differential equation (PDE) as a system of ordinary differential equations (ODE). The efficient fourth-order exponential time differencing Runge-Kutta (ETD-RK4) formula is utilized for solving this system. The main aim of this paper is to show that the integrated radial basis method based on the local form can be exerted for solving the coupled non-linear advection-diffusion-reaction system. The numerical tests are provided to illustrate its validity and accuracy.

用紧凑的局部综合径向基函数（CLIRBF）方法可以近似地计算出在防止地下水污染问题中产生的以对流为主的扩散反应方程。为了有效地求解对流扩散方程的非线性系统，我们使用积分径向基函数（IRBF）离散化空间变量。然后，通过线法（MOL）离散化所获得的常微分方程（ODE）的系统。MOL是将偏微分方程（PDE）视为常微分方程（ODE）系统的一种通用方法。利用有效的四阶指数时间微分Runge-Kutta（ETD-RK4）公式求解该系统。本文的主要目的是证明基于局部形式的综合径向基方法可用于求解非线性对流扩散反应系统。提供数值测试以说明其有效性和准确性。