Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations

Justin Mouyedo Loufouilou; Joseph Bonazebi Yindoula; Gabriel Bissanga

doi:doi:10.11648/j.ijamtp.20210701.14

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Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations

Justin Mouyedo Loufouilou, Joseph Bonazebi Yindoula, Gabriel Bissanga

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 7, Issue 1)

Received: 15 January 2021 Accepted: 8 March 2021 Published: 30 March 2021

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Abstract

Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 7, Issue 1)
DOI	10.11648/j.ijamtp.20210701.14
Page(s)	28-39
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

Adomian Decomposition Method, Systems of Differential Partial Equations, Coupled Partial Differential Equations

References

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Justin Mouyedo Loufouilou, Joseph Bonazebi Yindoula, Gabriel Bissanga. (2021). Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations. International Journal of Applied Mathematics and Theoretical Physics, 7(1), 28-39. https://doi.org/10.11648/j.ijamtp.20210701.14

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ACS Style

Justin Mouyedo Loufouilou; Joseph Bonazebi Yindoula; Gabriel Bissanga. Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations. Int. J. Appl. Math. Theor. Phys. 2021, 7(1), 28-39. doi: 10.11648/j.ijamtp.20210701.14

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AMA Style

Justin Mouyedo Loufouilou, Joseph Bonazebi Yindoula, Gabriel Bissanga. Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations. Int J Appl Math Theor Phys. 2021;7(1):28-39. doi: 10.11648/j.ijamtp.20210701.14

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@article{10.11648/j.ijamtp.20210701.14,
  author = {Justin Mouyedo Loufouilou and Joseph Bonazebi Yindoula and Gabriel Bissanga},
  title = {Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {7},
  number = {1},
  pages = {28-39},
  doi = {10.11648/j.ijamtp.20210701.14},
  url = {https://doi.org/10.11648/j.ijamtp.20210701.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20210701.14},
  abstract = {Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.},
 year = {2021}
}

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TY  - JOUR
T1  - Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations
AU  - Justin Mouyedo Loufouilou
AU  - Joseph Bonazebi Yindoula
AU  - Gabriel Bissanga
Y1  - 2021/03/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ijamtp.20210701.14
DO  - 10.11648/j.ijamtp.20210701.14
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 28
EP  - 39
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20210701.14
AB  - Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.
VL  - 7
IS  - 1
ER  -

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Author Information

Justin Mouyedo Loufouilou

Department of Exact Sciences, University Marien N’Gouabi, Brazzaville, Congo
Joseph Bonazebi Yindoula

Department of Exact Sciences, University Marien N’Gouabi, Brazzaville, Congo
Gabriel Bissanga

Department of Exact Sciences, University Marien N’Gouabi, Brazzaville, Congo

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APA Style

Justin Mouyedo Loufouilou, Joseph Bonazebi Yindoula, Gabriel Bissanga. (2021). Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations. International Journal of Applied Mathematics and Theoretical Physics, 7(1), 28-39. https://doi.org/10.11648/j.ijamtp.20210701.14

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ACS Style

Justin Mouyedo Loufouilou; Joseph Bonazebi Yindoula; Gabriel Bissanga. Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations. Int. J. Appl. Math. Theor. Phys. 2021, 7(1), 28-39. doi: 10.11648/j.ijamtp.20210701.14

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AMA Style

Justin Mouyedo Loufouilou, Joseph Bonazebi Yindoula, Gabriel Bissanga. Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations. Int J Appl Math Theor Phys. 2021;7(1):28-39. doi: 10.11648/j.ijamtp.20210701.14

Copy | Download

@article{10.11648/j.ijamtp.20210701.14,
  author = {Justin Mouyedo Loufouilou and Joseph Bonazebi Yindoula and Gabriel Bissanga},
  title = {Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {7},
  number = {1},
  pages = {28-39},
  doi = {10.11648/j.ijamtp.20210701.14},
  url = {https://doi.org/10.11648/j.ijamtp.20210701.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20210701.14},
  abstract = {Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations
AU  - Justin Mouyedo Loufouilou
AU  - Joseph Bonazebi Yindoula
AU  - Gabriel Bissanga
Y1  - 2021/03/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ijamtp.20210701.14
DO  - 10.11648/j.ijamtp.20210701.14
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 28
EP  - 39
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20210701.14
AB  - Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.
VL  - 7
IS  - 1
ER  -

Copy | Download