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 First order smooth composite Chebyshev finite difference method for solving coupled Lane-Emden problem in catalytic diffusion reactions

2021 ◽  
Vol 87 (2) ◽  
pp. 463-467
Author(s):  
Soner Aydinlik ◽  
◽  
Ahmet Kirisb
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Truncation Error ◽  
Continuity Condition ◽  
Effective Technique ◽  
First Order ◽  
Error Analyses ◽  
Chebyshev Finite Difference Method ◽  
Approximation Polynomial

A new effective technique based on Chebyshev Finite Difference Method is introduced. First order smoothness of the approximation polynomial at the end points of each sub-interval is imposed in addition to the continuity condition. Both round-off and truncation error analyses are given besides the convergence analysis. Coupled Lane Emden boundary value problem in Catalytic Diffusion Reactions is investigated by using presented 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 than the others.

scholarly journals Optimized Direct Padé and HPM for Solving Equation of Oxygen Diffusion in a Spherical Cell

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
M. A. Sandoval-Hernandez ◽  
H. Vazquez-Leal ◽  
A. Sarmiento-Reyes ◽  
U. Filobello-Nino ◽  
F. Castro-Gonzalez ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Oxygen Diffusion ◽  
Homotopy Perturbation Method ◽  
Oxygen Uptake Kinetics ◽  
Spherical Cell ◽  
Maximum Reaction Rate ◽  
Absolute Relative Error ◽  
Homotopy Perturbation ◽  
Maximum Reaction ◽  
Powerful Process

This work presents the application of homotopy perturbation method (HPM) and Optimized Direct Padé (ODP) to obtain a handy and easily computable approximate solution of the nonlinear differential equation to model the oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. On one hand, the obtained HPM solution is fully symbolic in terms of the coefficients of the equation, allowing us to use the same solution for different values of the maximum reaction rate, the Michaelis constant, and the permeability of the cell membrane. On the other hand, the numerical experiments show the high accuracy of the proposed ODP solution, resulting in 3.58×10-4 as the lowest absolute relative error (A.R.E.) for a set of coefficients. In addition, a novel technique is proposed to reduce the number of algebraic operations during the process of application of ODP method through the use of the Taylor series, which help to simplify the algebraic expressions used. The powerful process to obtain the solution shows that the Optimized Direct Padé and homotopy perturbation method are suitable methods to use.

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.

scholarly journals Modified Taylor solution of equation of oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics

2015 ◽  
Vol 4 (2) ◽  
pp. 253 ◽  
Author(s):  
Hector Vazquez-Leal ◽  
Mario Sandoval-Hernandez ◽  
Roberto Castaneda-Sheissa ◽  
Uriel Filobello-Nino ◽  
Arturo Sarmiento-Reyes
Keyword(s):  
Oxygen Diffusion ◽  
Spherical Cell ◽  
Uptake Kinetics

Sodium bicarbonate ingestion does not alter the slow component of oxygen uptake kinetics in professional cyclists

2003 ◽  
Vol 21 (1) ◽  
pp. 39-47 ◽  
Author(s):  
ALFREDO SANTALLA ◽  
MARGARITA PÉREZ ◽  
MANUEL MONTILLA ◽  
LÁZARO VICENTE ◽  
RICHARD DAVISON ◽  
...  
Keyword(s):  
Oxygen Uptake ◽  
Sodium Bicarbonate ◽  
Slow Component ◽  
Oxygen Uptake Kinetics ◽  
Uptake Kinetics
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