Solving Initial Value Problems by Flower Pollination Algorithm

Fatima Ouaar; Naceur Khelil

doi:doi:10.11648/j.ajece.20180202.14

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Solving Initial Value Problems by Flower Pollination Algorithm

Fatima Ouaar, Naceur Khelil

Published in American Journal of Electrical and Computer Engineering (Volume 2, Issue 2)

Received: 20 November 2018 Accepted: 13 December 2018 Published: 14 January 2019

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Abstract

Differential equations are very important in modeling many phenomena mathematically. The aim of this paper is to consider Initial Value Problems (IVPs) in ordinary differential equations (ODEs) as an optimization problem, solved by using a meta-heuristic algorithm which is considered as an alternative way to find numerical approximation of (IVPs) since they can almost be solved simply by classical mathematical tools which are not very precise. By selecting a methodical way based on the use of recent and efficient algorithm, that is, Flower Pollination Algorithm (FPA), inspired by the pollination process of flowers plants to solve approximately an (IVP) when a specified example is selected that is the exponential problem which have an imperative role to describe many real problems. The effectiveness of the proposed method is tested via a simulation study between the exact results, the FPA results and Euler method which is considerate as a classical tool to solve numerically an (IVP). The final results and after a comparison between the performance of FPA and Euler method in terms of solution quality shows that FPA yields satisfactorily precise approximation of the solution. That ensures the ability of FPA to solve such important problems and highly complexes problems efficiently with minimal error.

Published in	American Journal of Electrical and Computer Engineering (Volume 2, Issue 2)
DOI	10.11648/j.ajece.20180202.14
Page(s)	31-36
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), 2019. Published by Science Publishing Group

Keywords

Initial Value Problem (IVP), Optimization Problem, Exponential Model, Flower Pollination Algorithm (FPA)

References

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APA Style

Fatima Ouaar, Naceur Khelil. (2019). Solving Initial Value Problems by Flower Pollination Algorithm. American Journal of Electrical and Computer Engineering, 2(2), 31-36. https://doi.org/10.11648/j.ajece.20180202.14

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ACS Style

Fatima Ouaar; Naceur Khelil. Solving Initial Value Problems by Flower Pollination Algorithm. Am. J. Electr. Comput. Eng. 2019, 2(2), 31-36. doi: 10.11648/j.ajece.20180202.14

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AMA Style

Fatima Ouaar, Naceur Khelil. Solving Initial Value Problems by Flower Pollination Algorithm. Am J Electr Comput Eng. 2019;2(2):31-36. doi: 10.11648/j.ajece.20180202.14

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@article{10.11648/j.ajece.20180202.14,
  author = {Fatima Ouaar and Naceur Khelil},
  title = {Solving Initial Value Problems by Flower Pollination Algorithm},
  journal = {American Journal of Electrical and Computer Engineering},
  volume = {2},
  number = {2},
  pages = {31-36},
  doi = {10.11648/j.ajece.20180202.14},
  url = {https://doi.org/10.11648/j.ajece.20180202.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajece.20180202.14},
  abstract = {Differential equations are very important in modeling many phenomena mathematically. The aim of this paper is to consider Initial Value Problems (IVPs) in ordinary differential equations (ODEs) as an optimization problem, solved by using a meta-heuristic algorithm which is considered as an alternative way to find numerical approximation of (IVPs) since they can almost be solved simply by classical mathematical tools which are not very precise. By selecting a methodical way based on the use of recent and efficient algorithm, that is, Flower Pollination Algorithm (FPA), inspired by the pollination process of flowers plants to solve approximately an (IVP) when a specified example is selected that is the exponential problem which have an imperative role to describe many real problems. The effectiveness of the proposed method is tested via a simulation study between the exact results, the FPA results and Euler method which is considerate as a classical tool to solve numerically an (IVP). The final results and after a comparison between the performance of FPA and Euler method in terms of solution quality shows that FPA yields satisfactorily precise approximation of the solution. That ensures the ability of FPA to solve such important problems and highly complexes problems efficiently with minimal error.},
 year = {2019}
}

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TY  - JOUR
T1  - Solving Initial Value Problems by Flower Pollination Algorithm
AU  - Fatima Ouaar
AU  - Naceur Khelil
Y1  - 2019/01/14
PY  - 2019
N1  - https://doi.org/10.11648/j.ajece.20180202.14
DO  - 10.11648/j.ajece.20180202.14
T2  - American Journal of Electrical and Computer Engineering
JF  - American Journal of Electrical and Computer Engineering
JO  - American Journal of Electrical and Computer Engineering
SP  - 31
EP  - 36
PB  - Science Publishing Group
SN  - 2640-0502
UR  - https://doi.org/10.11648/j.ajece.20180202.14
AB  - Differential equations are very important in modeling many phenomena mathematically. The aim of this paper is to consider Initial Value Problems (IVPs) in ordinary differential equations (ODEs) as an optimization problem, solved by using a meta-heuristic algorithm which is considered as an alternative way to find numerical approximation of (IVPs) since they can almost be solved simply by classical mathematical tools which are not very precise. By selecting a methodical way based on the use of recent and efficient algorithm, that is, Flower Pollination Algorithm (FPA), inspired by the pollination process of flowers plants to solve approximately an (IVP) when a specified example is selected that is the exponential problem which have an imperative role to describe many real problems. The effectiveness of the proposed method is tested via a simulation study between the exact results, the FPA results and Euler method which is considerate as a classical tool to solve numerically an (IVP). The final results and after a comparison between the performance of FPA and Euler method in terms of solution quality shows that FPA yields satisfactorily precise approximation of the solution. That ensures the ability of FPA to solve such important problems and highly complexes problems efficiently with minimal error.
VL  - 2
IS  - 2
ER  -

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Author Information

Fatima Ouaar

Department of Mathematics, Faculty of Exact Sciences, Mohamed Khider University, Biskra, Algeria
Naceur Khelil

Department of Mathematics, Faculty of Exact Sciences, Mohamed Khider University, Biskra, Algeria

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APA Style

Fatima Ouaar, Naceur Khelil. (2019). Solving Initial Value Problems by Flower Pollination Algorithm. American Journal of Electrical and Computer Engineering, 2(2), 31-36. https://doi.org/10.11648/j.ajece.20180202.14

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ACS Style

Fatima Ouaar; Naceur Khelil. Solving Initial Value Problems by Flower Pollination Algorithm. Am. J. Electr. Comput. Eng. 2019, 2(2), 31-36. doi: 10.11648/j.ajece.20180202.14

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AMA Style

Fatima Ouaar, Naceur Khelil. Solving Initial Value Problems by Flower Pollination Algorithm. Am J Electr Comput Eng. 2019;2(2):31-36. doi: 10.11648/j.ajece.20180202.14

Copy | Download

@article{10.11648/j.ajece.20180202.14,
  author = {Fatima Ouaar and Naceur Khelil},
  title = {Solving Initial Value Problems by Flower Pollination Algorithm},
  journal = {American Journal of Electrical and Computer Engineering},
  volume = {2},
  number = {2},
  pages = {31-36},
  doi = {10.11648/j.ajece.20180202.14},
  url = {https://doi.org/10.11648/j.ajece.20180202.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajece.20180202.14},
  abstract = {Differential equations are very important in modeling many phenomena mathematically. The aim of this paper is to consider Initial Value Problems (IVPs) in ordinary differential equations (ODEs) as an optimization problem, solved by using a meta-heuristic algorithm which is considered as an alternative way to find numerical approximation of (IVPs) since they can almost be solved simply by classical mathematical tools which are not very precise. By selecting a methodical way based on the use of recent and efficient algorithm, that is, Flower Pollination Algorithm (FPA), inspired by the pollination process of flowers plants to solve approximately an (IVP) when a specified example is selected that is the exponential problem which have an imperative role to describe many real problems. The effectiveness of the proposed method is tested via a simulation study between the exact results, the FPA results and Euler method which is considerate as a classical tool to solve numerically an (IVP). The final results and after a comparison between the performance of FPA and Euler method in terms of solution quality shows that FPA yields satisfactorily precise approximation of the solution. That ensures the ability of FPA to solve such important problems and highly complexes problems efficiently with minimal error.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Solving Initial Value Problems by Flower Pollination Algorithm
AU  - Fatima Ouaar
AU  - Naceur Khelil
Y1  - 2019/01/14
PY  - 2019
N1  - https://doi.org/10.11648/j.ajece.20180202.14
DO  - 10.11648/j.ajece.20180202.14
T2  - American Journal of Electrical and Computer Engineering
JF  - American Journal of Electrical and Computer Engineering
JO  - American Journal of Electrical and Computer Engineering
SP  - 31
EP  - 36
PB  - Science Publishing Group
SN  - 2640-0502
UR  - https://doi.org/10.11648/j.ajece.20180202.14
AB  - Differential equations are very important in modeling many phenomena mathematically. The aim of this paper is to consider Initial Value Problems (IVPs) in ordinary differential equations (ODEs) as an optimization problem, solved by using a meta-heuristic algorithm which is considered as an alternative way to find numerical approximation of (IVPs) since they can almost be solved simply by classical mathematical tools which are not very precise. By selecting a methodical way based on the use of recent and efficient algorithm, that is, Flower Pollination Algorithm (FPA), inspired by the pollination process of flowers plants to solve approximately an (IVP) when a specified example is selected that is the exponential problem which have an imperative role to describe many real problems. The effectiveness of the proposed method is tested via a simulation study between the exact results, the FPA results and Euler method which is considerate as a classical tool to solve numerically an (IVP). The final results and after a comparison between the performance of FPA and Euler method in terms of solution quality shows that FPA yields satisfactorily precise approximation of the solution. That ensures the ability of FPA to solve such important problems and highly complexes problems efficiently with minimal error.
VL  - 2
IS  - 2
ER  -

Copy | Download