A Solution of one-dimensional ground water recharge through porous media via natural transform decomposition method and variational iteration transform method

Solution of one-dimensional ground water recharge through porous media

Abstract

In this paper, the application of the natural transform decomposition method (NTDM) and variational iteration transform method (VITM) is applied to obtain the solution for the one-dimensional ground water recharge through porous media in a fractional order with a singular kernel derivative. The one-dimensional groundwater recharge problem is a mathematical formulation derived assuming that the average coefficient of diffusivity remains constant across the entire moisture content range, while the permeability is allowed to vary. To obtain a solution, we employed the natural transform (NT) and Shehu transform (ST) in succession, followed by their inverse counterparts. The convergence and uniqueness of the solutions for the proposed methods have been analysed and discussed. The numerical simulations are provided to ensure that the methods under consideration are efficient. The current framework captures the behaviour of the obtained findings for various fractional orders. The findings of this study indicate that the proposed methods are effective and reliable in analyzing fractional differential equations. The obtained results demonstrate that the proposed methods are straightforward, highly accurate, and efficient.