Solution of Oxygen Diffusion Moving Boundary Value Problem Based on Variational Iteration Least Square Methods - I. Abdulhussein, Asmahan; S. Fadhel, Fadhel (Al-Nahrain Journal of Science, 2025)
This article aims to address and solve the oxygen diffusion problem which involves oxygen diffraction into a medium that absorbs and immobilizes the oxygen concentration at a constant rate. Such types of problems are difficult to solve analytically since it is a type of moving boundary value problem or one-phase Stefan problem, and such problems require us to determine the domain boundary as a part of the solution that is unknown or may vary with respect to time. The main governing equation, a partial differential equation used to govern the oxygen diffusion in an absorbing medium, is the heat equation, which has a moving boundary that varies with respect to time. Also, the presence of a moving boundary that indicates the farthest point where oxygen enters the medium, as well as, the initial distribution of oxygen across the medium will raise fundamental mathematical challenges in the solution. The approach followed for solving this problem is a semi-analytical method, which is a hybrid approach between the variational iteration method and the least squares method. These two methods are used to derive an efficient iterative approximate solution of the considered problem of this paper, because of their simplicity, efficiency and reliability in computational applications.