Euler’s Method for Solving Logistic Growth Model Using MATLAB

Desta Sodano Sheiso; Mekashew Ali Mohye

doi:doi:10.11648/j.ijssam.20220703.13

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Euler’s Method for Solving Logistic Growth Model Using MATLAB

Desta Sodano Sheiso, Mekashew Ali Mohye

Published in International Journal of Systems Science and Applied Mathematics (Volume 7, Issue 3)

Received: 2 June 2022 Accepted: 29 August 2022 Published: 16 September 2022

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Abstract

This paper introduces Euler’s explicit method for solving the numerical solution of the population growth model, logistic growth model. The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. Euler's method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can't be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations. To validate the applicability of the method on the proposed equation, a model example has been solved for different values of parameters. Using this balance law, we can develop the Logistic Model for population growth. For this model, we assume that we add population at a rate proportional to how many are already there. The numerical results in terms of point wise absolute errors presented in tables and graphs show that the present method approximates the exact solution very well. We discuss and explain the solution of logistic growth of population, the kinds of problems that arise in various fields of sciences and engineering. This study aims to solve numerically Euler’s method for solving using the Matlab.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 7, Issue 3)
DOI	10.11648/j.ijssam.20220703.13
Page(s)	60-65
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

Euler’s Explicit Method, Logistic Growth Model, Least Square Method, 6th Order RK Method, MATLAB

References

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[2]	K. W. Morton and D. F. Mayers, (2005). Numerical Solution of Partial Differential Equations, Second Edition, Cambridge University Press, New York.
[3]	Fred Brauer Carlos Castillo-Chavez, (2011). Mathematical Models in Population Biology and Epidemiology, Second Edition.
[4]	Frederick Adler. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists. Brooks/Cole, 2004.
[5]	Edward A. Bender. An Introduction to Mathematical Modeling. John Wiley & Sons, New YorkChichester-Brisbane, (1978). A Wiley-Interscience Publication.
[6]	Richard L. Burden and J. Douglas Faires. Numerical Analysis. Brooks/Cole, 6th edition, (1997).
[7]	Hal Caswell. Matrix Population Models: Construction, Analysis, and Interpretation. Sinauer Associates, Inc., Massachusetts, second edition, 2001.
[8]	Steven C. Chapra, (1998). Applied Numerical Methods with MATLAB for Engineers and Scientists. McGraw Hill Companies, Inc., New York, 2nd edition, 2008.
[9]	James L. Cornette and Ralph A, (2012). Ackerman. Calculus for the Life Sciences: A Modeling Approach, Volume I. Cornette and Ackerman, 2011.
[10]	Brenner, S. and Scott, L., (2008). The Mathematical Theory of Finite Element Methods, third edition, Springer-verlag.
[11]	William P. Fox. Mathematical Modeling with Maple. Brooks/Cole, Cengage Learning, Boston, 2012.
[12]	Joseph M. Mahaffy, (2010). Calculus for the life sciences i, lecture notes- discrete malthusian growth.
[13]	Daniel Maki and Maynard Thompson, (2003). Mathematical Modeling and Computer Simulation. Brooks/Cole, 2006.
[14]	The Mathworks, Inc., Natick, Massachusetts. MATLAB version 9.10.0.1649659 (R2021a) Update 1, 2021.
[15]	Cleve B. Moler. Numerical Computing with Matlab. The MathWorks, Inc., Natik, 2004.
[16]	Douglas D. Mooney and Randall J. Swift, (2011). A Course in Mathematical Modeling. Classroom Resource Materials Series. Mathematical Association of America, Washington, DC, 1999.

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Desta Sodano Sheiso, Mekashew Ali Mohye. (2022). Euler’s Method for Solving Logistic Growth Model Using MATLAB. International Journal of Systems Science and Applied Mathematics, 7(3), 60-65. https://doi.org/10.11648/j.ijssam.20220703.13

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ACS Style

Desta Sodano Sheiso; Mekashew Ali Mohye. Euler’s Method for Solving Logistic Growth Model Using MATLAB. Int. J. Syst. Sci. Appl. Math. 2022, 7(3), 60-65. doi: 10.11648/j.ijssam.20220703.13

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AMA Style

Desta Sodano Sheiso, Mekashew Ali Mohye. Euler’s Method for Solving Logistic Growth Model Using MATLAB. Int J Syst Sci Appl Math. 2022;7(3):60-65. doi: 10.11648/j.ijssam.20220703.13

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@article{10.11648/j.ijssam.20220703.13,
  author = {Desta Sodano Sheiso and Mekashew Ali Mohye},
  title = {Euler’s Method for Solving Logistic Growth Model Using MATLAB},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {7},
  number = {3},
  pages = {60-65},
  doi = {10.11648/j.ijssam.20220703.13},
  url = {https://doi.org/10.11648/j.ijssam.20220703.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20220703.13},
  abstract = {This paper introduces Euler’s explicit method for solving the numerical solution of the population growth model, logistic growth model. The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. Euler's method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can't be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations. To validate the applicability of the method on the proposed equation, a model example has been solved for different values of parameters. Using this balance law, we can develop the Logistic Model for population growth. For this model, we assume that we add population at a rate proportional to how many are already there. The numerical results in terms of point wise absolute errors presented in tables and graphs show that the present method approximates the exact solution very well. We discuss and explain the solution of logistic growth of population, the kinds of problems that arise in various fields of sciences and engineering. This study aims to solve numerically Euler’s method for solving using the Matlab.},
 year = {2022}
}

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TY  - JOUR
T1  - Euler’s Method for Solving Logistic Growth Model Using MATLAB
AU  - Desta Sodano Sheiso
AU  - Mekashew Ali Mohye
Y1  - 2022/09/16
PY  - 2022
N1  - https://doi.org/10.11648/j.ijssam.20220703.13
DO  - 10.11648/j.ijssam.20220703.13
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 60
EP  - 65
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20220703.13
AB  - This paper introduces Euler’s explicit method for solving the numerical solution of the population growth model, logistic growth model. The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. Euler's method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can't be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations. To validate the applicability of the method on the proposed equation, a model example has been solved for different values of parameters. Using this balance law, we can develop the Logistic Model for population growth. For this model, we assume that we add population at a rate proportional to how many are already there. The numerical results in terms of point wise absolute errors presented in tables and graphs show that the present method approximates the exact solution very well. We discuss and explain the solution of logistic growth of population, the kinds of problems that arise in various fields of sciences and engineering. This study aims to solve numerically Euler’s method for solving using the Matlab.
VL  - 7
IS  - 3
ER  -

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Author Information

Desta Sodano Sheiso

Department of Mathematics, Collage of Natural and Computational Science, Wolkite University, Wolkite, Ethiopia
Mekashew Ali Mohye

Department of Mathematics, Collage of Natural and Computational Science, Wolkite University, Wolkite, Ethiopia

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Plain Text BibTeX RIS

APA Style

Desta Sodano Sheiso, Mekashew Ali Mohye. (2022). Euler’s Method for Solving Logistic Growth Model Using MATLAB. International Journal of Systems Science and Applied Mathematics, 7(3), 60-65. https://doi.org/10.11648/j.ijssam.20220703.13

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ACS Style

Desta Sodano Sheiso; Mekashew Ali Mohye. Euler’s Method for Solving Logistic Growth Model Using MATLAB. Int. J. Syst. Sci. Appl. Math. 2022, 7(3), 60-65. doi: 10.11648/j.ijssam.20220703.13

Copy | Download

AMA Style

Desta Sodano Sheiso, Mekashew Ali Mohye. Euler’s Method for Solving Logistic Growth Model Using MATLAB. Int J Syst Sci Appl Math. 2022;7(3):60-65. doi: 10.11648/j.ijssam.20220703.13

Copy | Download

@article{10.11648/j.ijssam.20220703.13,
  author = {Desta Sodano Sheiso and Mekashew Ali Mohye},
  title = {Euler’s Method for Solving Logistic Growth Model Using MATLAB},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {7},
  number = {3},
  pages = {60-65},
  doi = {10.11648/j.ijssam.20220703.13},
  url = {https://doi.org/10.11648/j.ijssam.20220703.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20220703.13},
  abstract = {This paper introduces Euler’s explicit method for solving the numerical solution of the population growth model, logistic growth model. The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. Euler's method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can't be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations. To validate the applicability of the method on the proposed equation, a model example has been solved for different values of parameters. Using this balance law, we can develop the Logistic Model for population growth. For this model, we assume that we add population at a rate proportional to how many are already there. The numerical results in terms of point wise absolute errors presented in tables and graphs show that the present method approximates the exact solution very well. We discuss and explain the solution of logistic growth of population, the kinds of problems that arise in various fields of sciences and engineering. This study aims to solve numerically Euler’s method for solving using the Matlab.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Euler’s Method for Solving Logistic Growth Model Using MATLAB
AU  - Desta Sodano Sheiso
AU  - Mekashew Ali Mohye
Y1  - 2022/09/16
PY  - 2022
N1  - https://doi.org/10.11648/j.ijssam.20220703.13
DO  - 10.11648/j.ijssam.20220703.13
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 60
EP  - 65
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20220703.13
AB  - This paper introduces Euler’s explicit method for solving the numerical solution of the population growth model, logistic growth model. The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. Euler's method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can't be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations. To validate the applicability of the method on the proposed equation, a model example has been solved for different values of parameters. Using this balance law, we can develop the Logistic Model for population growth. For this model, we assume that we add population at a rate proportional to how many are already there. The numerical results in terms of point wise absolute errors presented in tables and graphs show that the present method approximates the exact solution very well. We discuss and explain the solution of logistic growth of population, the kinds of problems that arise in various fields of sciences and engineering. This study aims to solve numerically Euler’s method for solving using the Matlab.
VL  - 7
IS  - 3
ER  -

Copy | Download