In this study, we simulate numerically the process of oxygen mass transport in the human circulatory system incorporating the contribution of axial diffusion. Simulated equation is a time dependent convective-diffusion partial differential equation wherein has applicable application in the bioengineering problems such as boundary layer of fluids, electrical circuits in cables and mass transport problems.
The analytical solution of this kind of equations is complicated. Therefore, the numerical solution for obtaining the approximate solution is important and the convergence and stability in this method of solution, is always a question. In this study, we try to answer the above questions with respect to this special equation and for this we use finite differences.

Keywords: Unsteady partial differential equation, Finite difference method, Consistent, Stability, Convergence

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