Du Fort-Frankel Finite Difference Scheme for Solving of Oxygen Diffusion Problem Inside One Cell

Abstract In this paper, we use the well-known Du Fort-Frankel finite difference scheme to solve the oxygen diffusion problem inside one cell which is modeled by an initial moving boundary value problem for one dimensional time-dependent partial differential equation. The main problem consists in tracking the moving boundary that represents the oxygen penetration depth inside the cell. We explore the possibilities of numerical approximation of the problem posed by the different formulations. Some numerical experiments are also provided with comparisons with analytical solution.The theoretical analysis is given for the numerical scheme. It is shown that all the results obtained by this method are compared with earlier authors. AMS Subject Classification: 35R35; 35R37; 80A22; 65M06; 65N06.