Comparative study between two numerical methods for oxygen diffusion problem

Abstract

SUMMARYTwo 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.

The oxygen diffusion problem: Analysis and numerical solution

“…There is, by now, an extensive literature on numerical solutions to the oxygen diffusion problem [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Crank and Gupta [1] considered integral methods, more commonly referred to as heat balance integral methods in relation to heat conduction problems, but these were not valid for small times and also broke down before all the oxygen had been depleted.…”

Solution of fractional oxygen diffusion problem having without singular kernel

“…In this direction Noble suggested the repeated spatial subdivision [20], the heat balance integral method defined by Reynolds and Dalton [22], an orthogonal collocation for solving the partial differential equation of the diffusion of oxygen in absorbing tissue described by Liapis et al [16]. Two numerical methods for solving the oxygen diffusion problem were proposed by Gülkaç [14]. Mitchell studied the accurate application of the integral method [19].…”

The New Approximate Analytic Solution for Oxygen Diffusion Problem with Time-Fractional Derivative

“…Noble [3] suggested repeated spatial subdivision, Reynolds and Dolton [4] also developed the heat balance integral method, and Liapis et al [5] proposed an orthogonal collocation for solving the partial differential equation of the diffusion of oxygen in absorbing tissue. Gülkaç proposed two numerical methods for solving the oxygen diffusion problem [6]. Mitchell studied the accurate application of the integral method [7].…”