Solutions of Ordinary Differential System by Using Symmetry Group

Sameer Qasim Hasan; Wissam Salman Abd

doi:doi:10.11648/j.ajam.20160404.14

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Solutions of Ordinary Differential System by Using Symmetry Group

Sameer Qasim Hasan, Wissam Salman Abd

Published in American Journal of Applied Mathematics (Volume 4, Issue 4)

Received: 19 June 2016 Accepted: 28 June 2016 Published: 28 July 2016

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Abstract

In this paper the idea is to use a coordinate transformation that takes a system of ordinary differential equations with no obvious solution to system of integrables. The techniques that which introduced presented the cases of symmetry transformations also the particular case that involving an integrating factory homogeneous coordinates all these transformations are interest in lie groups theory.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 4)
DOI	10.11648/j.ajam.20160404.14
Page(s)	186-191
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

Coordinate Transformation, System Ordinary Differential Equations, Symmetry Transformation, Lie Groups Theory

References

[1]	Zachary Martinot. (2014). Solutions to Ordinary Differential Equations Using Methods of Symmetry.
[2]	Oliver, P. J. (2000). Applications of Lie groups to differential equations (Vol. 107). Springer.
[3]	Starrett, J. (2007). Solving differential equations by Symmetry groups. The American Mathematical Monthly, 778-792.
[4]	Oliveri F. (2010). Lie Symmetries of differential equations: Classical results and recent contributions. symmetry open access Journals 2, volume 2, pp. 758-706.
[5]	John Starrett. Solving Differential Equations by Symmetry Groups.
[6]	Jacob Harry Burkman. (2007). Symmetry group solutions to differential equations.
[7]	Peter J. Olver and Philip Rosenau. (1987). Group-Invariant solutions of differential equations.
[8]	E. S. Cheb-Terrab and T. Kolokolnikov. (2002). First- order ordinary differential equations symmetry and linear transformations.
[9]	Mehmet can. (1996). Lie symmetries of differential equations by computer algebra.
[10]	G. W. Bluman and S. Kumei. (1989).Symmetries and differential equations.

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Sameer Qasim Hasan, Wissam Salman Abd. (2016). Solutions of Ordinary Differential System by Using Symmetry Group. American Journal of Applied Mathematics, 4(4), 186-191. https://doi.org/10.11648/j.ajam.20160404.14

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ACS Style

Sameer Qasim Hasan; Wissam Salman Abd. Solutions of Ordinary Differential System by Using Symmetry Group. Am. J. Appl. Math. 2016, 4(4), 186-191. doi: 10.11648/j.ajam.20160404.14

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AMA Style

Sameer Qasim Hasan, Wissam Salman Abd. Solutions of Ordinary Differential System by Using Symmetry Group. Am J Appl Math. 2016;4(4):186-191. doi: 10.11648/j.ajam.20160404.14

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@article{10.11648/j.ajam.20160404.14,
  author = {Sameer Qasim Hasan and Wissam Salman Abd},
  title = {Solutions of Ordinary Differential System by Using Symmetry Group},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {4},
  pages = {186-191},
  doi = {10.11648/j.ajam.20160404.14},
  url = {https://doi.org/10.11648/j.ajam.20160404.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160404.14},
  abstract = {In this paper the idea is to use a coordinate transformation that takes a system of ordinary differential equations with no obvious solution to system of integrables. The techniques that which introduced presented the cases of symmetry transformations also the particular case that involving an integrating factory homogeneous coordinates all these transformations are interest in lie groups theory.},
 year = {2016}
}

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TY  - JOUR
T1  - Solutions of Ordinary Differential System by Using Symmetry Group
AU  - Sameer Qasim Hasan
AU  - Wissam Salman Abd
Y1  - 2016/07/28
PY  - 2016
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DO  - 10.11648/j.ajam.20160404.14
T2  - American Journal of Applied Mathematics
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JO  - American Journal of Applied Mathematics
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AB  - In this paper the idea is to use a coordinate transformation that takes a system of ordinary differential equations with no obvious solution to system of integrables. The techniques that which introduced presented the cases of symmetry transformations also the particular case that involving an integrating factory homogeneous coordinates all these transformations are interest in lie groups theory.
VL  - 4
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Author Information

Sameer Qasim Hasan

Department of Mathematical, College of Education, Almustansryah University, Baghdad, Iraq
Wissam Salman Abd

Department of Mathematical, College of Education, Almustansryah University, Baghdad, Iraq

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APA Style

Sameer Qasim Hasan, Wissam Salman Abd. (2016). Solutions of Ordinary Differential System by Using Symmetry Group. American Journal of Applied Mathematics, 4(4), 186-191. https://doi.org/10.11648/j.ajam.20160404.14

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ACS Style

Sameer Qasim Hasan; Wissam Salman Abd. Solutions of Ordinary Differential System by Using Symmetry Group. Am. J. Appl. Math. 2016, 4(4), 186-191. doi: 10.11648/j.ajam.20160404.14

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AMA Style

Sameer Qasim Hasan, Wissam Salman Abd. Solutions of Ordinary Differential System by Using Symmetry Group. Am J Appl Math. 2016;4(4):186-191. doi: 10.11648/j.ajam.20160404.14

Copy | Download

@article{10.11648/j.ajam.20160404.14,
  author = {Sameer Qasim Hasan and Wissam Salman Abd},
  title = {Solutions of Ordinary Differential System by Using Symmetry Group},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {4},
  pages = {186-191},
  doi = {10.11648/j.ajam.20160404.14},
  url = {https://doi.org/10.11648/j.ajam.20160404.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160404.14},
  abstract = {In this paper the idea is to use a coordinate transformation that takes a system of ordinary differential equations with no obvious solution to system of integrables. The techniques that which introduced presented the cases of symmetry transformations also the particular case that involving an integrating factory homogeneous coordinates all these transformations are interest in lie groups theory.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Solutions of Ordinary Differential System by Using Symmetry Group
AU  - Sameer Qasim Hasan
AU  - Wissam Salman Abd
Y1  - 2016/07/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160404.14
DO  - 10.11648/j.ajam.20160404.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 186
EP  - 191
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160404.14
AB  - In this paper the idea is to use a coordinate transformation that takes a system of ordinary differential equations with no obvious solution to system of integrables. The techniques that which introduced presented the cases of symmetry transformations also the particular case that involving an integrating factory homogeneous coordinates all these transformations are interest in lie groups theory.
VL  - 4
IS  - 4
ER  -

Copy | Download