A semi-analytic method to solve the oxygen diffusion problem

In this paper, a semi-analytic approach is proposed to solve the oxygen diffusion problem.First, we discretize the partial differential equation of the oxygen diffusion problem in temporal direction using the backward finite difference Euler method. We achieve a sequence of free boundary problems in the form of ordinary differential equations (ODEs) in the spatial direction. The ODEs are then solved analytically and a recursive formula is presented to compute the solutions of the ordinary differential equations. The problems of finding unknown boundaries are reduced to nonlinear algebraic problems. Finally, the nonlinear algebraic problems are solved using the root-finding methods such as the false position method. The method proposed in this paper is easy to implement and a comparison with other numerical methods shows that the proposed approach is very efficient and gives very accurate numerical results.Some tables and figures are included to show the efficiency and effectiveness of the proposed technique.