Compact local integrated radial basis functions (Integrated RBF) method for solving system of non-linear advection-diffusion-reaction equations to prevent the groundwater contamination

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.