A reliable analysis of oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics

2014 ◽  
Vol 07 (02) ◽  
pp. 1450020 ◽  
Author(s):  
Randolph Rach ◽  
Abdul-Majid Wazwaz ◽  
Jun-Sheng Duan
Keyword(s):  
Boundary Condition ◽  
Adomian Decomposition Method ◽  
Integral Form ◽  
Oxygen Uptake Kinetics ◽  
Spherical Cell ◽  
Uptake Kinetics ◽  
Intermediate Step ◽  
Unknown Constant ◽  
Emden Equation ◽  
Adomian Decomposition

In this paper, we investigate the diffusion of oxygen in a spherical cell including nonlinear uptake kinetics. The Lane–Emden boundary value problem with Michaelis–Menten kinetics is used to model the dimensionless oxygen concentration in our analysis. We first convert the Lane–Emden equation to the equivalent Volterra integral form that incorporates the boundary condition at the cell's center, but which still leaves one unknown constant of integration, as an intermediate step. Next we evaluate the Volterra integral form of the concentration and its flux at the cell membrane and substitute them into the remaining boundary condition to determine the unknown constant of integration by appropriate algebraic manipulations. Upon substitution we have converted the equivalent Volterra integral form to the equivalent Fredholm–Volterra integral form, and use the Duan–Rach modified recursion scheme to effectively decompose the unknown constant of integration by formula. The Adomian decomposition method is then applied to solve the equivalent nonlinear Fredholm–Volterra integral representation of the Lane–Emden model for the concentration of oxygen within the spherical cell. Our approach shows enhancements over existing techniques.

Oxygen diffusion in a spherical cell subject to nonlinear Michaelis–Menten kinetics: Mathematical analysis by two exact methods

2017 ◽  
Vol 10 (02) ◽  
pp. 1750025
Author(s):  
Hooman Fatoorehchi ◽  
Hossein Abolghasemi ◽  
Laura Villafuerte ◽  
Reza Zarghami
Keyword(s):  
Oxygen Diffusion ◽  
Adomian Decomposition Method ◽  
Spherical Cell ◽  
Time Analysis ◽  
Exact Methods ◽  
Perfect Agreement ◽  
Transform Method ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Differential Transform

A nonlinear model representing oxygen diffusion accompanied by the Michaelis–Menten consumption kinetics inside a spherical cell is solved analytically by the differential transform method (DTM) and the modified Adomian decomposition method (MADM). A perfect agreement between the literature data and the results from the proposed solutions is found. The advantages and drawbacks of the two approaches are discussed and their efficiencies are compared through a CPU-time analysis.

Solution of Fractional Diffusion Equation with a Moving Boundary Condition by Variational Iteration Method and Adomian Decomposition Method

2010 ◽  
Vol 65 (10) ◽  
pp. 793-799 ◽  
Author(s):  
Subir Das ◽  
Subir Rajeev
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Iteration Method ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Fractional Diffusion ◽  
Adomian Decomposition ◽  
Moving Boundary Condition

In this paper, the approximate analytic solutions of the mathematical model of time fractional diffusion equation (FDE) with a moving boundary condition are obtained with the help of variational iteration method (VIM) and Adomian decomposition method (ADM). By using boundary conditions, the explicit solutions of the diffusion front and fractional releases in the dimensionless form have been derived. Both mathematical techniques used to solve the problem perform extremely well in terms of efficiency and simplicity. Numerical solutions of the problem show that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

An efficient method for oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics

2021 ◽  
Author(s):  
Soner Aydinlik
Keyword(s):  
Oxygen Diffusion ◽  
Truncation Error ◽  
Numerical Technique ◽  
Oxygen Uptake Kinetics ◽  
Spherical Cell ◽  
Uptake Kinetics ◽  
First Order ◽  
Error Analyses ◽  
Approximation Polynomial ◽  
Order Smoothness

In this paper, a novel numerical technique, the first-order Smooth Composite Chebyshev Finite Difference method, is presented. Imposing a first-order smoothness of the approximation polynomial at the ends of each subinterval is originality of the method. Both round-off and truncation error analyses of the method are performed beside the convergence analysis. Diffusion of oxygen in a spherical cell including nonlinear uptake kinetics is solved by using the method. The obtained results are compared with the existing methods in the literature and it is observed that the proposed method gives more reliable results.

scholarly journals Application of Adomian Decomposition Method to Bounded and Unbounded Stokes’ Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Chi-Min Liu ◽  
Ray-Yeng Yang
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Unknown Function ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Finite Depth ◽  
Adomian Decomposition ◽  
Stokes Problems ◽  
Mathematical Techniques ◽  
Expansion Point

The well-known Stokes’ problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes’ problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes’ problems of finite and infinite depths.

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