Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method

Mubushra Saleem; Tahira Amir; Qazi Mahmood Ul-Hassan; Kamran Ayub; Farhana Kanwal

doi:doi:10.11648/j.be.20170101.15

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Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method

Mubushra Saleem, Tahira Amir, Qazi Mahmood Ul-Hassan, Kamran Ayub, Farhana Kanwal

Published in Bioprocess Engineering (Volume 1, Issue 1)

Received: 26 March 2017 Accepted: 25 April 2017 Published: 22 June 2017

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Abstract

Solutions of nonlinear models are of great importance and their significance has increased a lot. In given paper, the homotopy perturbation method (HPM) is implemented to show the numerical assumption of the population dynamics model with density-dependent migeration and the Allee effect. The resemblance of the numerical solutions attained by HPM with exact solution allows the order of this method. The results show applicability, accuracy and efficiency of HPM in solving the parabolic equation. HPM is effective for solving the transitary non-linear advection diffusion reaction equation.

Published in	Bioprocess Engineering (Volume 1, Issue 1)
DOI	10.11648/j.be.20170101.15
Page(s)	30-34
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), 2017. Published by Science Publishing Group

Keywords

Homotopy Perturbation Method, Allee Effects, Density-Dependent Migeration, Maple 18

References

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[7]	M. Dehghan, F. Shakeri, Solution of an integro-differential equation arising in oscillating magnetic fields using He’s homotopy perturbation method, Progress in Electromagnetic Research, PIER, 78, (2008) 361-376.
[8]	M. Dehghan, F. Shakeri, Use of He’s homotpy perturbation method for solving a partial differential equation arising in modeling of flow in porous media, Journal of Porous Media, 11 (2008) 765-778.
[9]	A. Saadatmandi, M. Dehghan, A. Eftekhari, Application of He’s homotopy perturbation method for non-linear system of second-order boundary value problems, Nonlinear Analysis: Real World Applications, 10 (2009) 1912–1922.
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APA Style

Mubushra Saleem, Tahira Amir, Qazi Mahmood Ul-Hassan, Kamran Ayub, Farhana Kanwal. (2017). Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method. Bioprocess Engineering, 1(1), 30-34. https://doi.org/10.11648/j.be.20170101.15

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ACS Style

Mubushra Saleem; Tahira Amir; Qazi Mahmood Ul-Hassan; Kamran Ayub; Farhana Kanwal. Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method. Bioprocess Eng. 2017, 1(1), 30-34. doi: 10.11648/j.be.20170101.15

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AMA Style

Mubushra Saleem, Tahira Amir, Qazi Mahmood Ul-Hassan, Kamran Ayub, Farhana Kanwal. Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method. Bioprocess Eng. 2017;1(1):30-34. doi: 10.11648/j.be.20170101.15

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@article{10.11648/j.be.20170101.15,
  author = {Mubushra Saleem and Tahira Amir and Qazi Mahmood Ul-Hassan and Kamran Ayub and Farhana Kanwal},
  title = {Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method},
  journal = {Bioprocess Engineering},
  volume = {1},
  number = {1},
  pages = {30-34},
  doi = {10.11648/j.be.20170101.15},
  url = {https://doi.org/10.11648/j.be.20170101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.be.20170101.15},
  abstract = {Solutions of nonlinear models are of great importance and their significance has increased a lot. In given paper, the homotopy perturbation method (HPM) is implemented to show the numerical assumption of the population dynamics model with density-dependent migeration and the Allee effect. The resemblance of the numerical solutions attained by HPM with exact solution allows the order of this method. The results show applicability, accuracy and efficiency of HPM in solving the parabolic equation. HPM is effective for solving the transitary non-linear advection diffusion reaction equation.},
 year = {2017}
}

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TY  - JOUR
T1  - Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method
AU  - Mubushra Saleem
AU  - Tahira Amir
AU  - Qazi Mahmood Ul-Hassan
AU  - Kamran Ayub
AU  - Farhana Kanwal
Y1  - 2017/06/22
PY  - 2017
N1  - https://doi.org/10.11648/j.be.20170101.15
DO  - 10.11648/j.be.20170101.15
T2  - Bioprocess Engineering
JF  - Bioprocess Engineering
JO  - Bioprocess Engineering
SP  - 30
EP  - 34
PB  - Science Publishing Group
SN  - 2578-8701
UR  - https://doi.org/10.11648/j.be.20170101.15
AB  - Solutions of nonlinear models are of great importance and their significance has increased a lot. In given paper, the homotopy perturbation method (HPM) is implemented to show the numerical assumption of the population dynamics model with density-dependent migeration and the Allee effect. The resemblance of the numerical solutions attained by HPM with exact solution allows the order of this method. The results show applicability, accuracy and efficiency of HPM in solving the parabolic equation. HPM is effective for solving the transitary non-linear advection diffusion reaction equation.
VL  - 1
IS  - 1
ER  -

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Author Information

Mubushra Saleem

Department of Mathematics, University of Wah, Wah Cantt., Pakistan
Tahira Amir

Department of Mathematics, University of Wah, Wah Cantt., Pakistan
Qazi Mahmood Ul-Hassan

Department of Mathematics, University of Wah, Wah Cantt., Pakistan
Kamran Ayub

Department of Mathematics, Riphah International University, Islamabad, Pakistan
Farhana Kanwal

Department of Mathematics, Allama Iqbal Open University, Islamabad, Pakistan

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Plain Text BibTeX RIS

APA Style

Mubushra Saleem, Tahira Amir, Qazi Mahmood Ul-Hassan, Kamran Ayub, Farhana Kanwal. (2017). Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method. Bioprocess Engineering, 1(1), 30-34. https://doi.org/10.11648/j.be.20170101.15

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ACS Style

Mubushra Saleem; Tahira Amir; Qazi Mahmood Ul-Hassan; Kamran Ayub; Farhana Kanwal. Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method. Bioprocess Eng. 2017, 1(1), 30-34. doi: 10.11648/j.be.20170101.15

Copy | Download

AMA Style

Mubushra Saleem, Tahira Amir, Qazi Mahmood Ul-Hassan, Kamran Ayub, Farhana Kanwal. Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method. Bioprocess Eng. 2017;1(1):30-34. doi: 10.11648/j.be.20170101.15

Copy | Download

@article{10.11648/j.be.20170101.15,
  author = {Mubushra Saleem and Tahira Amir and Qazi Mahmood Ul-Hassan and Kamran Ayub and Farhana Kanwal},
  title = {Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method},
  journal = {Bioprocess Engineering},
  volume = {1},
  number = {1},
  pages = {30-34},
  doi = {10.11648/j.be.20170101.15},
  url = {https://doi.org/10.11648/j.be.20170101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.be.20170101.15},
  abstract = {Solutions of nonlinear models are of great importance and their significance has increased a lot. In given paper, the homotopy perturbation method (HPM) is implemented to show the numerical assumption of the population dynamics model with density-dependent migeration and the Allee effect. The resemblance of the numerical solutions attained by HPM with exact solution allows the order of this method. The results show applicability, accuracy and efficiency of HPM in solving the parabolic equation. HPM is effective for solving the transitary non-linear advection diffusion reaction equation.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Computing the Allee Effect and Population Dynamics with Density Dependent Migeration Using Homotopy Perturbation Method
AU  - Mubushra Saleem
AU  - Tahira Amir
AU  - Qazi Mahmood Ul-Hassan
AU  - Kamran Ayub
AU  - Farhana Kanwal
Y1  - 2017/06/22
PY  - 2017
N1  - https://doi.org/10.11648/j.be.20170101.15
DO  - 10.11648/j.be.20170101.15
T2  - Bioprocess Engineering
JF  - Bioprocess Engineering
JO  - Bioprocess Engineering
SP  - 30
EP  - 34
PB  - Science Publishing Group
SN  - 2578-8701
UR  - https://doi.org/10.11648/j.be.20170101.15
AB  - Solutions of nonlinear models are of great importance and their significance has increased a lot. In given paper, the homotopy perturbation method (HPM) is implemented to show the numerical assumption of the population dynamics model with density-dependent migeration and the Allee effect. The resemblance of the numerical solutions attained by HPM with exact solution allows the order of this method. The results show applicability, accuracy and efficiency of HPM in solving the parabolic equation. HPM is effective for solving the transitary non-linear advection diffusion reaction equation.
VL  - 1
IS  - 1
ER  -

Copy | Download