氧扩散问题两种数值方法的比较研究

Vildan Gülkaç
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引用次数: 9

摘要

利用三时间水平的Crank-Nicolson方程和三时间水平的隐式方法的Gauss-Seidel迭代定义了氧扩散问题的两个近似数值解。氧在细胞中的同步吸收扩散是一个重要的问题,具有广泛的医学应用。这个问题是通过两个不同的阶段用数学公式表述出来的。在第一阶段,搜索孤立细胞中没有氧跃迁的稳定情况,在第二阶段,搜索细胞内组织吸收氧的移动边界问题。采用三时间级隐式方法和三时间级隐式方法的Gauss-Seidel迭代得到的结果与以往的方法吻合较好(J. Inst. Appl.)。数学。1972;10:19-33;1974;13:385 - 398;1978;22:467 - 477)。版权所有©2008 John Wiley & Sons, Ltd
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Comparative study between two numerical methods for oxygen diffusion problem
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.
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