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

Authors

  • Hector Vazquez-Leal University of Veracruz, Electronic Instrumentation Faculty
  • Mario Sandoval-Hernandez University of Xalapa
  • Roberto Castaneda-Sheissa University of Veracruz, Electronic Instrumentation Faculty
  • Uriel Filobello-Nino University of Veracruz, Atmospheric Sciences Faculty
  • Arturo Sarmiento-Reyes National Institute for Astrophysics, Optics and Electronics

DOI:

https://doi.org/10.14419/ijamr.v4i2.4273

Published:

2015-03-09

Keywords:

Taylor method, Power series method, Boundary valued problems, Approximate solutions.

Abstract

This work presents the application of a modified Taylor method 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. The obtained solution is fully symbolic in terms of the coefficients of the equation, allowing to use the same solution for different values of the maximum reaction rate, the Michaelis constant, and the permeability of the cell membrane. Additionally, the numerical experiments show the high accuracy of the proposed solution, resulting 1.658509453Å~10−15 as the lowest mean square error for a set of coefficients. The straightforward process to obtain the solution shows that the modified Taylor method is a handy alternative to a more sophisticated method because does not involve the solving of differential equations or calculate complicated integrals.

References

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