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

Received date: February 2, 2015

Accepted date: February 11, 2015

Published date: March 9, 2015

DOI:

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

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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How to Cite

Vazquez-Leal, H., Sandoval-Hernandez, M., Castaneda-Sheissa, R., Filobello-Nino, U., & Sarmiento-Reyes, A. (2015). Modified Taylor solution of equation of oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics. International Journal of Applied Mathematical Research, 4(2), 253-258. https://doi.org/10.14419/ijamr.v4i2.4273

Received date: February 2, 2015

Accepted date: February 11, 2015

Published date: March 9, 2015