New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems

Kurunatha Perumal Thevar Vijayan Preethi; Rajaram Poovazhaki; Lakshmanan Rajendran

doi:doi:10.11648/j.acm.20170603.14

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New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems

Kurunatha Perumal Thevar Vijayan Preethi, Rajaram Poovazhaki, Lakshmanan Rajendran

Published in Applied and Computational Mathematics (Volume 6, Issue 3)

Received: 31 March 2017 Accepted: 17 April 2017 Published: 27 June 2017

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Abstract

In this paper, new homotopy perturbation method (iteration scheme) will be employed to solve the nonlinear dynamical problems that arise in thin membrane kinetics. More precisely, the method will be used to mathematically model and solve the kinetics of the thin membrane. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both mixed Dirichlet and Neumann boundary conditions are taken into consideration, while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Our analytical results are compared with numerical solution. The method is found to be easily implemented, fast, and computationally economical and attractive.

Published in	Applied and Computational Mathematics (Volume 6, Issue 3)
DOI	10.11648/j.acm.20170603.14
Page(s)	161-166
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), 2024. Published by Science Publishing Group

Keywords

Mathematical Modelling, Thin Membrane, Enzyme Kinetics, Homotopy Perturbation Method

References

[1]	He J. H., “Variational iteration method: A kind of nonlinear analytical technique” Some examples, Int. J. NonLinear Mech., 34(4), 699-708 (1999).
[2]	He J. H., “Homotopy perturbation technique”, Comput Methods Appl. Mech. Engng., 178(3), 257-262 (1999).
[3]	He J. H., “Application of homotopy perturbation method to nonlinear wave equations”, Chaos Solit. Fract., 26(3), 695-700 (2005).
[4]	S. S. Nourazar, M. Soori and A. Nazari-Golshan, “On the exact solution of Newell-Whitehead-Segel equation using the homotopy perturbation method”, Aust. J. Basic Appl. Sci., 5(8), 1400-1411(2011).
[5]	S. S. Nourazar, M. Soori and A. Nazari-Golshan, “On the exact solution of Burgers-Huxley equation using the homotopy perturbation method”, J. Appl. Math. Phy., 3(3), 285-294 (2015).
[6]	S. S. Nourazar, M. Soori and A. Nazari-Golshan, “On the homotopy perturbation method for the exact solution of Fitzhugh–Nagumo equation”, Int. J. Math. Computation, 27(1), 32-43 (2015).
[7]	R. Abazari and M. Abazari, “ Numerical study of Burgers–Huxley equations via reduced differential transform method”, Computat. Appl. Math., 32(1), 1-17 (2013).
[8]	J. Saranya, L. Rajendran, L. Wang,C. Fernandez, “A new mathematical modelling using homotopy perturbation method to solve nonlinear equations in enzymatic glucose fuel cells”, Chemical Physics Letters, 317–326,662(2016).
[9]	S. S. Ray and A. K. Gupta, “Comparative analysis of variational iteration method and Haar wavelet method for the numerical solutions of Burgers–Huxley and Huxley equations”, J. Math. Chemistry, 52(4), 1066-1080 (2014).
[10]	S. S. Nourazar, M. Soori and A. Nazari-Golshan, “Application of the variational iteration method and the homotopy perturbation method to the Fisher Type Equation”, Int. J. Math. Computation, 27(3), 1-9 (2015).
[11]	M. Soori, “The homotopy perturbation method and the variational iteration method to nonlinear differential equations”, (2011).
[12]	M. Soori, “Series solution of weakly-singular kernel volterra integro-differential equations by the combined laplace-adomian method”, (2016).
[13]	M. Soori, “The variational iteration method for the Newell-Whitehead-Segel equation”, (2016).
[14]	R. MaliniDevi, S. Pavithra, R. Saravanakumar, L. Rajendran, “Analysis of nonlinear vibrations of single walled carbon nanotubes”, International Journal of Modern Engineering Research (IJMER), 2249–6645, 6(11)(2016).
[15]	A. Eswari, L. Rajendran, “Analyticalexpressions of concentration and current in homogeneous catalytic reactions at spherical microelectrodes: Homotopy Perturbation approach”, Journal of Electroanalytical Chemistry, 173-184, 651(2011).
[16]	S. Thiagarajan A. Meena S. Anitha, L. Rajendran, “Analytical expression of the steady-state catalytic current of mediated bioelectro catalysis and the application of He’s Homotopy perturbation method”, J Math Chem, 96-104, 6(2) 2011.
[17]	Abbasbandy and Elyas Shivanian “Application of variational iteration method for nth-order integro-differential equations”, Zeitschrift für Naturforschung A 64 (7-8), 439-444
[18]	Saeid Abbasbandy and Elyas Shivanian, “Application of the variational iteration method for system of nonlinear Volterra’s integro-differential equations”, Mathematical and computational applications 14 (2), 147-158.
[19]	Hossein Vosughi and Elyas Shivanian, “A new analytical technique to solve Volterra's integral equations, Mathematical methods in the applied sciences” 34 (10), 1243-1253.
[20]	S. Abbasbandy, E. Magyari, E. Shivanian, “The homotopy analysis method for multiple solutions of nonlinear boundary value problems”, Communications in Nonlinear Science and Numerical Simulation 14 (9), 3530-3536.
[21]	Saeid Abbasbandy and Elyas Shivanian, “Prediction of multiplicity of solutions of nonlinear boundary value problems: novel application of homotopy analysis method”, Communications in Nonlinear Science and Numerical Simulation 15 (12), 3830-3846.
[22]	Saeid Abbasbandy and Elyas Shivanian, “Solution of singular linear vibrational BVPs by the homotopy analysis method”, Journal of Numerical Mathematics and Stochastics 1 (1), 77-84.
[23]	L. Ahmad Soltani’s, Elyas Shivanian, Reza Ezzati, “Convection–radiation heat transfer in solar heat exchangers filled with a porous medium: exact and shooting homotopy analysis solution”, Applied Thermal Engineering 103, 537-542.
[24]	Elyas Shivanian and S. J. Hosseini Ghoncheh, “A new branch solution for the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient”, The European Physical Journal Plus 132 (2), 97.

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Kurunatha Perumal Thevar Vijayan Preethi, Rajaram Poovazhaki, Lakshmanan Rajendran. (2017). New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems. Applied and Computational Mathematics, 6(3), 161-166. https://doi.org/10.11648/j.acm.20170603.14

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ACS Style

Kurunatha Perumal Thevar Vijayan Preethi; Rajaram Poovazhaki; Lakshmanan Rajendran. New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems. Appl. Comput. Math. 2017, 6(3), 161-166. doi: 10.11648/j.acm.20170603.14

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AMA Style

Kurunatha Perumal Thevar Vijayan Preethi, Rajaram Poovazhaki, Lakshmanan Rajendran. New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems. Appl Comput Math. 2017;6(3):161-166. doi: 10.11648/j.acm.20170603.14

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@article{10.11648/j.acm.20170603.14,
  author = {Kurunatha Perumal Thevar Vijayan Preethi and Rajaram Poovazhaki and Lakshmanan Rajendran},
  title = {New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {3},
  pages = {161-166},
  doi = {10.11648/j.acm.20170603.14},
  url = {https://doi.org/10.11648/j.acm.20170603.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170603.14},
  abstract = {In this paper, new homotopy perturbation method (iteration scheme) will be employed to solve the nonlinear dynamical problems that arise in thin membrane kinetics. More precisely, the method will be used to mathematically model and solve the kinetics of the thin membrane. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both mixed Dirichlet and Neumann boundary conditions are taken into consideration, while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Our analytical results are compared with numerical solution. The method is found to be easily implemented, fast, and computationally economical and attractive.},
 year = {2017}
}

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TY  - JOUR
T1  - New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems
AU  - Kurunatha Perumal Thevar Vijayan Preethi
AU  - Rajaram Poovazhaki
AU  - Lakshmanan Rajendran
Y1  - 2017/06/27
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170603.14
DO  - 10.11648/j.acm.20170603.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 161
EP  - 166
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170603.14
AB  - In this paper, new homotopy perturbation method (iteration scheme) will be employed to solve the nonlinear dynamical problems that arise in thin membrane kinetics. More precisely, the method will be used to mathematically model and solve the kinetics of the thin membrane. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both mixed Dirichlet and Neumann boundary conditions are taken into consideration, while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Our analytical results are compared with numerical solution. The method is found to be easily implemented, fast, and computationally economical and attractive.
VL  - 6
IS  - 3
ER  -

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Author Information

Kurunatha Perumal Thevar Vijayan Preethi

Department of Mathematics, E. M. G. Yadava Women’s College, Madurai, Tamilnadu, India
Rajaram Poovazhaki

Department of Mathematics, E. M. G. Yadava Women’s College, Madurai, Tamilnadu, India
Lakshmanan Rajendran

Department of Mathematics, Sethu Institute of Technology, Kariyapatty, Tamilnadu, India

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APA Style

Kurunatha Perumal Thevar Vijayan Preethi, Rajaram Poovazhaki, Lakshmanan Rajendran. (2017). New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems. Applied and Computational Mathematics, 6(3), 161-166. https://doi.org/10.11648/j.acm.20170603.14

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ACS Style

Kurunatha Perumal Thevar Vijayan Preethi; Rajaram Poovazhaki; Lakshmanan Rajendran. New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems. Appl. Comput. Math. 2017, 6(3), 161-166. doi: 10.11648/j.acm.20170603.14

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AMA Style

Kurunatha Perumal Thevar Vijayan Preethi, Rajaram Poovazhaki, Lakshmanan Rajendran. New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems. Appl Comput Math. 2017;6(3):161-166. doi: 10.11648/j.acm.20170603.14

Copy | Download

@article{10.11648/j.acm.20170603.14,
  author = {Kurunatha Perumal Thevar Vijayan Preethi and Rajaram Poovazhaki and Lakshmanan Rajendran},
  title = {New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {3},
  pages = {161-166},
  doi = {10.11648/j.acm.20170603.14},
  url = {https://doi.org/10.11648/j.acm.20170603.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170603.14},
  abstract = {In this paper, new homotopy perturbation method (iteration scheme) will be employed to solve the nonlinear dynamical problems that arise in thin membrane kinetics. More precisely, the method will be used to mathematically model and solve the kinetics of the thin membrane. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both mixed Dirichlet and Neumann boundary conditions are taken into consideration, while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Our analytical results are compared with numerical solution. The method is found to be easily implemented, fast, and computationally economical and attractive.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - New Approach of Homotopy Perturbation Method for Solving the Equations in Enzyme Biochemical Systems
AU  - Kurunatha Perumal Thevar Vijayan Preethi
AU  - Rajaram Poovazhaki
AU  - Lakshmanan Rajendran
Y1  - 2017/06/27
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170603.14
DO  - 10.11648/j.acm.20170603.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 161
EP  - 166
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170603.14
AB  - In this paper, new homotopy perturbation method (iteration scheme) will be employed to solve the nonlinear dynamical problems that arise in thin membrane kinetics. More precisely, the method will be used to mathematically model and solve the kinetics of the thin membrane. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both mixed Dirichlet and Neumann boundary conditions are taken into consideration, while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Our analytical results are compared with numerical solution. The method is found to be easily implemented, fast, and computationally economical and attractive.
VL  - 6
IS  - 3
ER  -

Copy | Download