Comparative study between two numerical methods for oxygen diffusion problem

Abstract

Two approximate numerical solutions of the oxygen diffusion problem are defined using three time-level of Crank–Nicolson equation and Gauss–Seidel iteration for three time-level of implicit method. Oxygen diffusion in a sike cell with simultaneous absorption is an important problem and has a wide range of medical applications. The problem is mathematically formulated through two different stages. At the first stage, the stable case having no oxygen transition in the isolated cell is searched, whereas at the second stage the moving boundary problem of oxygen absorbed by the tissues in the cell is searched. The results obtained by three time-level of implicit method and Gauss–Seidel iteration for three time-level of implicit method and the results gave a good agreement with the previous methods (J. Inst. Appl. Math. 1972; 10:19–33; 1974; 13:385–398; 1978; 22:467–477). Copyright © 2008 John Wiley & Sons, Ltd.