VARIATIONAL ITERATION METHOD AND ANALYTIC SOLUTION FOR LAPLACE EQUATION FOR STEADY GROUNDWATER FLOW

Abstract

In this paper, we present a new approach for solving the Laplace equation for steady groundwater flow using the Variational Iteration Method (VIM) and Analytic Solution. The Laplace equation is a fundamental equation that describes the behavior of groundwater flow in porous media. However, the analytical solution for this equation is not always possible, especially for complex geometries and boundary conditions. Finding a solution to the Laplace equation for steady groundwater flow in a given domain with certain boundary conditions is the stated problem. The strategy utilized in this study comprises using the VIM to solve the Laplace equation in series. A variety of differential equations can be solved using the VIM, which is a strong and effective method. In this study, we present the results of our analysis for different boundary conditions and geometries. The results show that the VIM is an effective method for solving the Laplace equation for steady groundwater flow. The solutions obtained with the VIM are compared with the analytic solutions, and good agreement is observed. In conclusion, the VIM and Analytic Solution approach is a promising method for solving the Laplace equation for steady groundwater flow. The results obtained with this method can be used to design and optimize groundwater remediation systems and to study the behavior of groundwater flow in complex geometries.