Optimized direct Padé and HPM for solving equation of oxygen diffusion in a spherical cell
type: Item
instance of: scholarly article
title: Optimized direct Padé and HPM for solving equation of oxygen diffusion in a spherical cell
zbMATH Open document ID: 1417.92226
DOI: 10.1155/2018/9142124
author: U. Filobello-Nino
author: R. A. Callejas-Molina
author: R. Ruiz-Gomez
author: Mario A. Sandoval-Hernandez
author: H. Vázquez-Leal
author: A. Sarmiento-Reyes
author: Francisco J. Castro-Gonzalez
author: A. L. Herrera-May
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: 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 \(3.58 \times 1 0^{- 4}\) 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.
Mathematics Subject Classification ID: 92E20
zbMATH DE Number: 7026720
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9142124
OpenAlex ID: W2889027902
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description: scientific article; zbMATH DE number 7026720