Partial Differential Equations in Applied Mathematics (Dec 2023)
A theoretical investigation of steady-state concentration processes at a carrier-mediated transport model using Akbari-Ganji and differential transform methods
Abstract
In this article, a carrier-mediated transport model is considered. The steady-state non-linear diffusion equations were solved by two effective and accessible analytical methods, Akbari-Ganji and the differential transform methods. Here, we present the generalized approximate analytical solution for the substrate, product, and reactant concentrations for the small experimental values of the kinetic and diffusion parameters. The numerical solution to this problem was derived using the Mat-lab/Scilab program, showing a satisfactory agreement between the analytical and numerical/computational outcomes. The simulated results can be compared to the relevant theories. This result through the physical parameters shows that the Akbari-Ganji method is better than the differential transform method. The effects of this study are applicable across the entire solution domain. Furthermore, the concentration of species, facilitation factor F, and the reaction equilibrium constant K are compared to the parameters are also obtained.
