Mathematical analysis of the resolution of the saltwater intrusion problem in a coastal aquifer using the RBF collocation method

Abstract

Contamination of drinking water sources can result from the issue of saltwater intrusion into freshwater aquifers. Because of the compatibility produced by the mathematical model of saltwater intrusion, many researchers employ the finite element or finite volume method to arrive at the outcome. In this paper, we proposed to develop a mathematical analysis to solve the mathematical model describing the saltwater intrusion phenomenon using the radial basis function collocation method, which is a mesh-free technique for numerical solving. The simplified version of the problem has been taken into consideration. We constructed the RBF scheme and employed Newton’s technique to solve the nonlinear system of equations it generated, as long as the RBF approach makes use of simply distributed nodes. The RBF scheme obtained is robust and requires knowledge of the computer programming language.