HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism

H. Vazquez-Leal; L. Hernandez-Martinez; Y. Khan; V.M. Jimenez-Fernandez; U. Filbello-Nino; A. Diaz-Sanchez; A.L. Herrera-May; R. Castaneda-Sheissa; A. Marin-Hernandez; F. Rabago-Bernal; J. Huerta-Chua; S.F. Hernandez-Machuca

doi:doi:10.11648/j.ajam.20140201.15

HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism

H. Vazquez-Leal, L. Hernandez-Martinez, Y. Khan, V.M. Jimenez-Fernandez, U. Filbello-Nino, A. Diaz-Sanchez, A.L. Herrera-May, R. Castaneda-Sheissa, A. Marin-Hernandez, F. Rabago-Bernal, J. Huerta-Chua, S.F. Hernandez-Machuca

Published in American Journal of Applied Mathematics (Volume 2, Issue 1)

Received: 14 February 2014 Published: 28 February 2014

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Abstract

In this paper, homotopy perturbation method (HPM) is employed to provide an approximate, but detailed, solution for the nonlinear differential equation that describes the calcium stimulated calcium release mechanism. Comparison to the exact solutions shows that the method is extremely efficient, if initial guess is suitably chosen.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 1)
DOI	10.11648/j.ajam.20140201.15
Page(s)	29-35
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Cellular Signaling, CICR Calcium Mechanism, Homotopy Perturbation Method

References

[1]	J.D. Murray, "Mathematical Biology: I. An Introduction", Springer, 3rd edition, December, 2007.
[2]	J. Keener, J. Sneyd, "Mathematical Physiology", Springer, October, 1998.
[3]	R. Resnick, D. Halliday, "FísicaVol 1", John Wiley and Sons, Inc., 1977.
[4]	G. Odell, G.F. Oster, B. Burnside, P. Alberch, "The mechanical basis for morphogenesis", Developmental Biology, vol. 85, pp. 446-462, 1981.
[5]	J.D. Murray, G.F. Oster, "Cell traction models for generating pattern and form in morphogenesis", Journal of Mathematical Biology, vol. 19, num. 3, 265-279, 1986.
[6]	A. Cheer, R. Nuccitelli, G.F. Oster, J.P. Vincent, "Cortical activity in vertebrate eggs I: The activation waves", Journal of Theoretical Biology, vol. 124, num. 4, pp. 377-404, 1987.
[7]	D.C. Lane, J.D. Murray, V.S. Manoranjan, "Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilisation waves on eggs", IMA Journal of Mathematics Applied in Medicine and Biology", vol. 4, pp. 309-331, 1987.
[8]	G.F. Simmons, "Differential equations with applications and historical notes", McGraw-Hill, 2nd edition, 1991.
[9]	J.H. He, "A coupling method of a homotopy technique and a perturbation technique for nonlinear problems" International Journal of Non-Linear Mechanics, vol. 351, pp. 37-43, 2000.
[10]	J.H. He, "Homotopy perturbation technique", Computational Methods in Applied Mechanics and Engineering, vol. 178, num. 3-4, pp. 257-262, August, 1999.
[11]	L.M.B. Assas, "Approximate solutions for the generalized kdv Burgers’ equation by He’s variational iteration method", PhysicaScripta, vol. 76, num. 2, pp. 161-164, 2007.
[12]	J.H. He, "Variational approach for nonlinear oscillators", Chaos, Solitons and Fractals, vol. 34, num. 5, pp.1430-1439, 2007.
[13]	D.J. Evans, K.R. Raslan, "The Tanh function method for solving some important nonlinear partial differential", International Journal of Computer Mathematics, vol. 82, pp. 897-905, 2005.
[14]	F. Xu, "A generalized soliton solution of the Konopelchenko-Dubrovsky Equation using He’s exp-function method", Z. Naturforsch, vol. 62a, pp. 685-688, 2007.
[15]	G. Adomain, "A review of decomposition method in applied mathematics", Journal of Mathematical Analysis and Applications, vol. 135, num. 2, pp. 501-544, 1988.
[16]	E. Babolian, J. Biazar, "On the order of convergence of Adomian method", Applied Mathematics and Computation, vol. 130, num. 2, pp. 383-387, 2002.
[17]	L.N. Zhang, L. Xu, "Determination of the limit cycle by He’s parameter expansion for oscillators in a potential", Z. Naturforsch, vol. 62a, pp. 396-398, 2007.
[18]	J.H. He, "Homotopy perturbation method for solving boundary value problems", Physics Letters A, vol. 350, num. 1-2, pp. 87-88, 2006.
[19]	A. Fereidoon, Y. Rostamiyan, M. Akbarzade, D.D. Ganji, "Application of He’s homotopy perturbation method to nonlinear shock damper dynamics", Archive of Applied Mechanics, vol. 80, num. 6, pp. 641-649, 2010.
[20]	J.H. He, "Recent development of the homotopy perturbation method", Topological Methods in Nonlinear Analysis, vol. 31, num. 2, pp. 205-209, 2008.
[21]	A. Beléndez, C. Pascual, M.L. Álvarez, D.I. Méndez, M.S. Yebra, A. Hernández, "Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method", PhysicaScripta, vol. 79, num. 1, pp. 1-24, 2009.
[22]	J.H. He, "A coupling method of a homotopy and a perturbation technique for nonlinear problems", International Journal of Non-Linear Mechanics, vol. 35, num. 1, pp. 37-43, 2000.
[23]	M. El .Shaed, "Application of He’s homotopy perturbation method to Volterra’sintegro differential equation", International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, num. 2, pp. 163-168, 2005.
[24]	J.H. He, "Some Asymptotic Methods for Strongly Nonlinear Equations", International Journal of Modern Physics B, vol. 20, num. 10, pp. 1141-1199, 2006.

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APA Style

H. Vazquez-Leal, L. Hernandez-Martinez, Y. Khan, V.M. Jimenez-Fernandez, U. Filbello-Nino, et al. (2014). HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism. American Journal of Applied Mathematics, 2(1), 29-35. https://doi.org/10.11648/j.ajam.20140201.15

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ACS Style

H. Vazquez-Leal; L. Hernandez-Martinez; Y. Khan; V.M. Jimenez-Fernandez; U. Filbello-Nino, et al. HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism. Am. J. Appl. Math. 2014, 2(1), 29-35. doi: 10.11648/j.ajam.20140201.15

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AMA Style

H. Vazquez-Leal, L. Hernandez-Martinez, Y. Khan, V.M. Jimenez-Fernandez, U. Filbello-Nino, et al. HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism. Am J Appl Math. 2014;2(1):29-35. doi: 10.11648/j.ajam.20140201.15

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@article{10.11648/j.ajam.20140201.15,
  author = {H. Vazquez-Leal and L. Hernandez-Martinez and Y. Khan and V.M. Jimenez-Fernandez and U. Filbello-Nino and A. Diaz-Sanchez and A.L. Herrera-May and R. Castaneda-Sheissa and A. Marin-Hernandez and F. Rabago-Bernal and J. Huerta-Chua and S.F. Hernandez-Machuca},
  title = {HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {1},
  pages = {29-35},
  doi = {10.11648/j.ajam.20140201.15},
  url = {https://doi.org/10.11648/j.ajam.20140201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140201.15},
  abstract = {In this paper, homotopy perturbation method (HPM) is employed to provide an approximate, but detailed, solution for the nonlinear differential equation that describes the calcium stimulated calcium release mechanism. Comparison to the exact solutions shows that the method is extremely efficient, if initial guess is suitably chosen.},
 year = {2014}
}

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TY  - JOUR
T1  - HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism
AU  - H. Vazquez-Leal
AU  - L. Hernandez-Martinez
AU  - Y. Khan
AU  - V.M. Jimenez-Fernandez
AU  - U. Filbello-Nino
AU  - A. Diaz-Sanchez
AU  - A.L. Herrera-May
AU  - R. Castaneda-Sheissa
AU  - A. Marin-Hernandez
AU  - F. Rabago-Bernal
AU  - J. Huerta-Chua
AU  - S.F. Hernandez-Machuca
Y1  - 2014/02/28
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140201.15
DO  - 10.11648/j.ajam.20140201.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 29
EP  - 35
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140201.15
AB  - In this paper, homotopy perturbation method (HPM) is employed to provide an approximate, but detailed, solution for the nonlinear differential equation that describes the calcium stimulated calcium release mechanism. Comparison to the exact solutions shows that the method is extremely efficient, if initial guess is suitably chosen.
VL  - 2
IS  - 1
ER  -

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Author Information

H. Vazquez-Leal

Electronic Instrumentation, Universidad Veracruzana, Xalapa, Veracruz, Mexico
L. Hernandez-Martinez

National Institute for Astrophysics, Optics and Electronics, Sta. Maria Tonantzintla, Puebla, Mexico
Y. Khan

Department of Mathematics, Zhejiang University, Hangzhou, China
V.M. Jimenez-Fernandez

Electronic Instrumentation, Universidad Veracruzana, Xalapa, Veracruz, Mexico
U. Filbello-Nino

Electronic Instrumentation, Universidad Veracruzana, Xalapa, Veracruz, Mexico
A. Diaz-Sanchez

National Institute for Astrophysics, Optics and Electronics, Sta. Maria Tonantzintla, Puebla, Mexico
A.L. Herrera-May

Micro and NanotechnologyResearch Center, Universidad Veracruzana, Boca del Rio, Veracruz, Mexico
R. Castaneda-Sheissa

Electronic Instrumentation, Universidad Veracruzana, Xalapa, Veracruz, Mexico
A. Marin-Hernandez

Department of Artificial Intelligence, Universidad Veracruzana, Xalapa, Veracruz, Mexico
F. Rabago-Bernal

Institute of Physics, AutonomousUniversity of San Luis Potosi, San Luis Potosi, SLP, Mexico
J. Huerta-Chua

Civil EngineeringSchool, Universidad Veracruzana, Poza Rica, Veracruz, Mexico
S.F. Hernandez-Machuca

Electronic Instrumentation, Universidad Veracruzana, Xalapa, Veracruz, Mexico

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Plain Text BibTeX RIS

APA Style

H. Vazquez-Leal, L. Hernandez-Martinez, Y. Khan, V.M. Jimenez-Fernandez, U. Filbello-Nino, et al. (2014). HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism. American Journal of Applied Mathematics, 2(1), 29-35. https://doi.org/10.11648/j.ajam.20140201.15

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ACS Style

H. Vazquez-Leal; L. Hernandez-Martinez; Y. Khan; V.M. Jimenez-Fernandez; U. Filbello-Nino, et al. HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism. Am. J. Appl. Math. 2014, 2(1), 29-35. doi: 10.11648/j.ajam.20140201.15

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AMA Style

H. Vazquez-Leal, L. Hernandez-Martinez, Y. Khan, V.M. Jimenez-Fernandez, U. Filbello-Nino, et al. HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism. Am J Appl Math. 2014;2(1):29-35. doi: 10.11648/j.ajam.20140201.15

Copy | Download

@article{10.11648/j.ajam.20140201.15,
  author = {H. Vazquez-Leal and L. Hernandez-Martinez and Y. Khan and V.M. Jimenez-Fernandez and U. Filbello-Nino and A. Diaz-Sanchez and A.L. Herrera-May and R. Castaneda-Sheissa and A. Marin-Hernandez and F. Rabago-Bernal and J. Huerta-Chua and S.F. Hernandez-Machuca},
  title = {HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {1},
  pages = {29-35},
  doi = {10.11648/j.ajam.20140201.15},
  url = {https://doi.org/10.11648/j.ajam.20140201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140201.15},
  abstract = {In this paper, homotopy perturbation method (HPM) is employed to provide an approximate, but detailed, solution for the nonlinear differential equation that describes the calcium stimulated calcium release mechanism. Comparison to the exact solutions shows that the method is extremely efficient, if initial guess is suitably chosen.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - HPM Method Applied to Solve the Model of Calcium Stimulated, Calcium Release Mechanism
AU  - H. Vazquez-Leal
AU  - L. Hernandez-Martinez
AU  - Y. Khan
AU  - V.M. Jimenez-Fernandez
AU  - U. Filbello-Nino
AU  - A. Diaz-Sanchez
AU  - A.L. Herrera-May
AU  - R. Castaneda-Sheissa
AU  - A. Marin-Hernandez
AU  - F. Rabago-Bernal
AU  - J. Huerta-Chua
AU  - S.F. Hernandez-Machuca
Y1  - 2014/02/28
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140201.15
DO  - 10.11648/j.ajam.20140201.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 29
EP  - 35
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140201.15
AB  - In this paper, homotopy perturbation method (HPM) is employed to provide an approximate, but detailed, solution for the nonlinear differential equation that describes the calcium stimulated calcium release mechanism. Comparison to the exact solutions shows that the method is extremely efficient, if initial guess is suitably chosen.
VL  - 2
IS  - 1
ER  -

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