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

AbstractIn 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.Keywords: Stefan problemsmoving boundary problemspartial differential equationsDu Fort-Frankel finite difference schemefinite difference methodsAMS SUBJECT CLASSIFICATION: 35R3535R3780A2265M0665N06 AcknowledgementsThe work described in this paper was supported by the research grant of Ferhat Abbas University Sétif 1 and From Algerian Ministry of Higher Education and Scientific Research (Project(PRFU) code. C00L03UN190120190002). Finally, the author is grateful to the referee for the careful reading of the paper and all useful suggestions and comments.Disclosure statementNo potential conflict of interest was reported by the authors.