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**A numerical method for oxygen diffusion and absorption in a sike cell.**
*(English)*
Zbl 1090.65115

Summary: Oxygen diffusion in a sike cell with simultaneous absorption is an important problem and has a wide range of medical applications. The problem mathematically formulated through two different stages, the present paper, concerns mainly on the second stage, in which, the injected oxygen through the cell starts absorbing. The basic idea of the proposed numerical method is to form a double linear system of equations, each of dimension (\(4 \times 4\)).

The first system is formed through applying first, second, third and fourth moments and using assumed profile for the concentration containing four unknowns functions of time. Numerical solution through a proposed scheme leads to the unknown functions. The second system is formed through applying the boundary conditions given in addition to another assumed condition, that is the concentration at \(x = 0\) is an unknown function of time. The results of the first system becomes an entry data for the second one leading to the concentration at the fixed surface \(x = 0\). The result obtained by the present method are compared with two different methods and the results give a good agreement.

The first system is formed through applying first, second, third and fourth moments and using assumed profile for the concentration containing four unknowns functions of time. Numerical solution through a proposed scheme leads to the unknown functions. The second system is formed through applying the boundary conditions given in addition to another assumed condition, that is the concentration at \(x = 0\) is an unknown function of time. The results of the first system becomes an entry data for the second one leading to the concentration at the fixed surface \(x = 0\). The result obtained by the present method are compared with two different methods and the results give a good agreement.

### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

35K05 | Heat equation |

### Keywords:

moving boundary problem; Euler equation; integral equation method; algorithm; numerical examples; oxygen diffusion
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\textit{S. G. Ahmed}, Appl. Math. Comput. 173, No. 1, 668--682 (2006; Zbl 1090.65115)

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### References:

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