A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method

Bazuaye Frank Etin-Osa; Omoregbe Osahon Charles

doi:doi:10.11648/j.pamj.20221101.11

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A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method

Bazuaye Frank Etin-Osa, Omoregbe Osahon Charles

Published in Pure and Applied Mathematics Journal (Volume 11, Issue 1)

Received: 14 December 2021 Accepted: 17 January 2022 Published: 25 January 2022

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Abstract

In this work, a numerical analysis of a mathematical model for the preservation of forestry biomass is investigated. The model is divided into three compartments as density of forest biomass, density of wood based industries and density of synthetic industries. The Laplace Decomposition Method is used to obtain approximate solutions in the form of infinite series. Numerical justification is performed on the model parameter values with the aid of Maple 18 software to obtain the results. The behavior of the results obtained, is presented graphically. From the results, it was observed that the population of forest biomass increases exponentially as we increase the competitive effect of forest biomass c₁, on wood industries. It was also observed that the wood based industries will have no depleting effect on the forest biomass even when the competitive effect parameter of wood based industries c₂, on forest biomass was increased, and this was likened to increase awareness on synthetics as alternatives to wood, government control policies on deforestation, and an increase in prices of timber. It was also obvious from the result that as sufficient synthetic materials are supplied to the synthetic industries, the industries explode exponentially with time, and would serve as a good alternative to wood inpreserving the forestry biomass.

Published in	Pure and Applied Mathematics Journal (Volume 11, Issue 1)
DOI	10.11648/j.pamj.20221101.11
Page(s)	1-19
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), 2022. Published by Science Publishing Group

Keywords

Biomass, Infinite Series, Laplace Decomposition, Density

References

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[5]	Teru, A. H., and Koya, P. R. (2020). Mathematical Modelling of Deforestation of Forested Area Due to Lack of Awareness of Human Population and Its Conservation. Mathematical Modelling and Applications, 5 (2), 94-104.
[6]	Muhammad, F., Muhammad U. S., Aqeel A., and Ahmad, M. O. (2018). Analysis and numerical solution of SEIR epidermic model of measles with non-integer time fractional derivatives by using Laplace Adomian Decomposition Method. Ain Shams Engineering Journal, 9 (4), 3391-3397.
[7]	Chaudhary, M., Dhar, J. (2013). Forestry Biomass Conservation with Synthetic Industry: A Mathematical Model. Nirma University International Conference on Engineering (NUiCONE), https://doi.org/10.1109/NUiCONE.2013.6780205.
[8]	Rachana, P. (2018). Depletion of Forest Resources and Wildlife Population with Habitat Complexity: A Mathematical Model. Open Journal of Ecology, 8 (11), 579-589.
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[10]	Agyemang I., and Freedom H. I. (2009). An environmental model for the interaction of industry with two competing agricultural resources. Mathematical and Computing Modelling: An International Journal, 49 (7), 1618-1643.
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[14]	Lata, K., Dubey, B., and Misra, A. K. (2016). Modelling the effects of wood and non-wood based industries of forestry resources. Natural Resource Modelling, 29 (4), 559-580.
[15]	Elizabeth, S., Victor, P. (2018). A mathematical Model on Deforestation Due to Human Population and Its Effect on Farm Field: Role of Technology in its Conservation. Journal of Informatics and Mathematical Sciences, pp. 425-432.
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[17]	Bazuaye F. E. (2021). A Laplace Decomposition Analysis of Corona Virus Disease 2019 (COVID-19) Pandemic Model. International Journal of Mathematical Science and Optimization: Theory and Applications. Vol 6 (2): 847-861.
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APA Style

Bazuaye Frank Etin-Osa, Omoregbe Osahon Charles. (2022). A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method. Pure and Applied Mathematics Journal, 11(1), 1-19. https://doi.org/10.11648/j.pamj.20221101.11

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ACS Style

Bazuaye Frank Etin-Osa; Omoregbe Osahon Charles. A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method. Pure Appl. Math. J. 2022, 11(1), 1-19. doi: 10.11648/j.pamj.20221101.11

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AMA Style

Bazuaye Frank Etin-Osa, Omoregbe Osahon Charles. A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method. Pure Appl Math J. 2022;11(1):1-19. doi: 10.11648/j.pamj.20221101.11

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@article{10.11648/j.pamj.20221101.11,
  author = {Bazuaye Frank Etin-Osa and Omoregbe Osahon Charles},
  title = {A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method},
  journal = {Pure and Applied Mathematics Journal},
  volume = {11},
  number = {1},
  pages = {1-19},
  doi = {10.11648/j.pamj.20221101.11},
  url = {https://doi.org/10.11648/j.pamj.20221101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221101.11},
  abstract = {In this work, a numerical analysis of a mathematical model for the preservation of forestry biomass is investigated. The model is divided into three compartments as density of forest biomass, density of wood based industries and density of synthetic industries. The Laplace Decomposition Method is used to obtain approximate solutions in the form of infinite series. Numerical justification is performed on the model parameter values with the aid of Maple 18 software to obtain the results. The behavior of the results obtained, is presented graphically. From the results, it was observed that the population of forest biomass increases exponentially as we increase the competitive effect of forest biomass c1, on wood industries. It was also observed that the wood based industries will have no depleting effect on the forest biomass even when the competitive effect parameter of wood based industries c2, on forest biomass was increased, and this was likened to increase awareness on synthetics as alternatives to wood, government control policies on deforestation, and an increase in prices of timber. It was also obvious from the result that as sufficient synthetic materials are supplied to the synthetic industries, the industries explode exponentially with time, and would serve as a good alternative to wood inpreserving the forestry biomass.},
 year = {2022}
}

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TY  - JOUR
T1  - A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method
AU  - Bazuaye Frank Etin-Osa
AU  - Omoregbe Osahon Charles
Y1  - 2022/01/25
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221101.11
DO  - 10.11648/j.pamj.20221101.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 19
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20221101.11
AB  - In this work, a numerical analysis of a mathematical model for the preservation of forestry biomass is investigated. The model is divided into three compartments as density of forest biomass, density of wood based industries and density of synthetic industries. The Laplace Decomposition Method is used to obtain approximate solutions in the form of infinite series. Numerical justification is performed on the model parameter values with the aid of Maple 18 software to obtain the results. The behavior of the results obtained, is presented graphically. From the results, it was observed that the population of forest biomass increases exponentially as we increase the competitive effect of forest biomass c1, on wood industries. It was also observed that the wood based industries will have no depleting effect on the forest biomass even when the competitive effect parameter of wood based industries c2, on forest biomass was increased, and this was likened to increase awareness on synthetics as alternatives to wood, government control policies on deforestation, and an increase in prices of timber. It was also obvious from the result that as sufficient synthetic materials are supplied to the synthetic industries, the industries explode exponentially with time, and would serve as a good alternative to wood inpreserving the forestry biomass.
VL  - 11
IS  - 1
ER  -

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Author Information

Bazuaye Frank Etin-Osa

Department of Mathematics and Statistics, Faculty of Science, University of Port Harcourt, Port Harcourt, Nigeria
Omoregbe Osahon Charles

Department of Mathematics and Statistics, Faculty of Science, University of Port Harcourt, Port Harcourt, Nigeria

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Plain Text BibTeX RIS

APA Style

Bazuaye Frank Etin-Osa, Omoregbe Osahon Charles. (2022). A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method. Pure and Applied Mathematics Journal, 11(1), 1-19. https://doi.org/10.11648/j.pamj.20221101.11

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ACS Style

Bazuaye Frank Etin-Osa; Omoregbe Osahon Charles. A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method. Pure Appl. Math. J. 2022, 11(1), 1-19. doi: 10.11648/j.pamj.20221101.11

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AMA Style

Bazuaye Frank Etin-Osa, Omoregbe Osahon Charles. A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method. Pure Appl Math J. 2022;11(1):1-19. doi: 10.11648/j.pamj.20221101.11

Copy | Download

@article{10.11648/j.pamj.20221101.11,
  author = {Bazuaye Frank Etin-Osa and Omoregbe Osahon Charles},
  title = {A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method},
  journal = {Pure and Applied Mathematics Journal},
  volume = {11},
  number = {1},
  pages = {1-19},
  doi = {10.11648/j.pamj.20221101.11},
  url = {https://doi.org/10.11648/j.pamj.20221101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221101.11},
  abstract = {In this work, a numerical analysis of a mathematical model for the preservation of forestry biomass is investigated. The model is divided into three compartments as density of forest biomass, density of wood based industries and density of synthetic industries. The Laplace Decomposition Method is used to obtain approximate solutions in the form of infinite series. Numerical justification is performed on the model parameter values with the aid of Maple 18 software to obtain the results. The behavior of the results obtained, is presented graphically. From the results, it was observed that the population of forest biomass increases exponentially as we increase the competitive effect of forest biomass c1, on wood industries. It was also observed that the wood based industries will have no depleting effect on the forest biomass even when the competitive effect parameter of wood based industries c2, on forest biomass was increased, and this was likened to increase awareness on synthetics as alternatives to wood, government control policies on deforestation, and an increase in prices of timber. It was also obvious from the result that as sufficient synthetic materials are supplied to the synthetic industries, the industries explode exponentially with time, and would serve as a good alternative to wood inpreserving the forestry biomass.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method
AU  - Bazuaye Frank Etin-Osa
AU  - Omoregbe Osahon Charles
Y1  - 2022/01/25
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221101.11
DO  - 10.11648/j.pamj.20221101.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 19
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20221101.11
AB  - In this work, a numerical analysis of a mathematical model for the preservation of forestry biomass is investigated. The model is divided into three compartments as density of forest biomass, density of wood based industries and density of synthetic industries. The Laplace Decomposition Method is used to obtain approximate solutions in the form of infinite series. Numerical justification is performed on the model parameter values with the aid of Maple 18 software to obtain the results. The behavior of the results obtained, is presented graphically. From the results, it was observed that the population of forest biomass increases exponentially as we increase the competitive effect of forest biomass c1, on wood industries. It was also observed that the wood based industries will have no depleting effect on the forest biomass even when the competitive effect parameter of wood based industries c2, on forest biomass was increased, and this was likened to increase awareness on synthetics as alternatives to wood, government control policies on deforestation, and an increase in prices of timber. It was also obvious from the result that as sufficient synthetic materials are supplied to the synthetic industries, the industries explode exponentially with time, and would serve as a good alternative to wood inpreserving the forestry biomass.
VL  - 11
IS  - 1
ER  -

Copy | Download