Application of the Differential Transform Method for the Nonlinear Differential Equations

Mohand M. Abdelrahim Mahgoub; Abdelbagy A. Alshikh

doi:doi:10.11648/j.ajam.20170501.12

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Application of the Differential Transform Method for the Nonlinear Differential Equations

Mohand M. Abdelrahim Mahgoub, Abdelbagy A. Alshikh

Published in American Journal of Applied Mathematics (Volume 5, Issue 1)

Received: 15 October 2016 Accepted: 28 October 2016 Published: 18 January 2017

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Abstract

This paper aims to find analytical solutions of some analytical solutions of some non-linear differential equations using a new integral transform ''Aboodh transform'' with the differential transform method. The nonlinear terms can be easily handled by the use of differential transform method. This method is more efficient and easy to handle such differential equations in comparison to other methods. The results reveal that this method is very efficient, simple and can be applied to other nonlinear problems

Published in	American Journal of Applied Mathematics (Volume 5, Issue 1)
DOI	10.11648/j.ajam.20170501.12
Page(s)	14-18
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), 2017. Published by Science Publishing Group

Keywords

Aboodh Transform, Differential Transform Method, Nonlinear Differential Equations

References

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[14]	A. Arikoglu, I. Ozkol, Solution of boundary value problem for integro-differential equations by using differential transform method, Appl. Math. Comput. 168 (2005) 1145-1158.
[15]	Badriah A. S. Alamri. Nonlinear Differential Equations and Mixture of Tarig Transform and Differential Transform Method, Journal of Progressive Research in Mathematics Volume 5, Issue 3.
[16]	Z. M. Odibat, Differential transform method for solving Volterra integral equations with separable kernels, Math. Comput. Model. 48 (7-8) (2008) 1144-1149.
[17]	K. S. Aboodh, The New Integral Transform “Aboodh Transform” Global Journal of pure and Applied Mathematics, 9 (1), 35-43 (2013).
[18]	K. S. Aboodh, Application of New Transform “Aboodh transform” to Partial Differential Equations, Global Journal of pure and Applied Math, 10 (2), 249-254(2014).
[19]	Mohand M. Abdelrahim Mahgob “ Homotopy Perturbation Method And Aboodh Transform For Solving Sine-Gorden And Klein – Gorden Equations” International Journal of Engineering Sciences & Research Technology, 5 (10): October, 2016.
[20]	Mohand M. Abdelrahim Mahgob and Abdelilah K. Hassan Sedeeg “The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method ” American Journal of Applied Mathematics 2016; 4 (5): 217-221.
[21]	Abdelilah K. Hassan Sedeeg and Mohand M. Abdelrahim Mahgoub, “ Aboodh Transform Homotopy Perturbation Method For Solving System Of Nonlinear Partial Differential Equations,” Mathematical Theory and Modeling Vol. 6, No. 8, 2016.
[22]	Abdelilah K. Hassan Sedeeg and Mohand M. Abdelrahim Mahgoub, “Combine Aboodh Transform And Homotopy Perturbation Method For Solving Linear And Nonlinear Schrodinger Equations,” International Journal of Development Research Vol. 06, Issue, 08, pp. 9085-9089, August, 2016.
[23]	Abdelbagy A. Alshikh and Mohand M. Abdelrahim Mahgoub, “A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform,” Pure and Applied Mathematics Journal 2016; 5 (5): 145-150.

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Mohand M. Abdelrahim Mahgoub, Abdelbagy A. Alshikh. (2017). Application of the Differential Transform Method for the Nonlinear Differential Equations. American Journal of Applied Mathematics, 5(1), 14-18. https://doi.org/10.11648/j.ajam.20170501.12

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ACS Style

Mohand M. Abdelrahim Mahgoub; Abdelbagy A. Alshikh. Application of the Differential Transform Method for the Nonlinear Differential Equations. Am. J. Appl. Math. 2017, 5(1), 14-18. doi: 10.11648/j.ajam.20170501.12

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AMA Style

Mohand M. Abdelrahim Mahgoub, Abdelbagy A. Alshikh. Application of the Differential Transform Method for the Nonlinear Differential Equations. Am J Appl Math. 2017;5(1):14-18. doi: 10.11648/j.ajam.20170501.12

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@article{10.11648/j.ajam.20170501.12,
  author = {Mohand M. Abdelrahim Mahgoub and Abdelbagy A. Alshikh},
  title = {Application of the Differential Transform Method for the Nonlinear Differential Equations},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {1},
  pages = {14-18},
  doi = {10.11648/j.ajam.20170501.12},
  url = {https://doi.org/10.11648/j.ajam.20170501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170501.12},
  abstract = {This paper aims to find analytical solutions of some analytical solutions of some non-linear differential equations using a new integral transform ''Aboodh transform'' with the differential transform method. The nonlinear terms can be easily handled by the use of differential transform method. This method is more efficient and easy to handle such differential equations in comparison to other methods. The results reveal that this method is very efficient, simple and can be applied to other nonlinear problems},
 year = {2017}
}

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TY  - JOUR
T1  - Application of the Differential Transform Method for the Nonlinear Differential Equations
AU  - Mohand M. Abdelrahim Mahgoub
AU  - Abdelbagy A. Alshikh
Y1  - 2017/01/18
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170501.12
DO  - 10.11648/j.ajam.20170501.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 14
EP  - 18
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170501.12
AB  - This paper aims to find analytical solutions of some analytical solutions of some non-linear differential equations using a new integral transform ''Aboodh transform'' with the differential transform method. The nonlinear terms can be easily handled by the use of differential transform method. This method is more efficient and easy to handle such differential equations in comparison to other methods. The results reveal that this method is very efficient, simple and can be applied to other nonlinear problems
VL  - 5
IS  - 1
ER  -

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Author Information

Mohand M. Abdelrahim Mahgoub

Department of Mathematics, Faculty of Science & Technology, Omdurman Islamic University, Khartoum, Sudan
Abdelbagy A. Alshikh

Mathematics Department Faculty of Education-Alzaeim Alazhari University, Khartoum, Sudan

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Mohand M. Abdelrahim Mahgoub, Abdelbagy A. Alshikh. (2017). Application of the Differential Transform Method for the Nonlinear Differential Equations. American Journal of Applied Mathematics, 5(1), 14-18. https://doi.org/10.11648/j.ajam.20170501.12

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ACS Style

Mohand M. Abdelrahim Mahgoub; Abdelbagy A. Alshikh. Application of the Differential Transform Method for the Nonlinear Differential Equations. Am. J. Appl. Math. 2017, 5(1), 14-18. doi: 10.11648/j.ajam.20170501.12

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AMA Style

Mohand M. Abdelrahim Mahgoub, Abdelbagy A. Alshikh. Application of the Differential Transform Method for the Nonlinear Differential Equations. Am J Appl Math. 2017;5(1):14-18. doi: 10.11648/j.ajam.20170501.12

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@article{10.11648/j.ajam.20170501.12,
  author = {Mohand M. Abdelrahim Mahgoub and Abdelbagy A. Alshikh},
  title = {Application of the Differential Transform Method for the Nonlinear Differential Equations},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {1},
  pages = {14-18},
  doi = {10.11648/j.ajam.20170501.12},
  url = {https://doi.org/10.11648/j.ajam.20170501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170501.12},
  abstract = {This paper aims to find analytical solutions of some analytical solutions of some non-linear differential equations using a new integral transform ''Aboodh transform'' with the differential transform method. The nonlinear terms can be easily handled by the use of differential transform method. This method is more efficient and easy to handle such differential equations in comparison to other methods. The results reveal that this method is very efficient, simple and can be applied to other nonlinear problems},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Application of the Differential Transform Method for the Nonlinear Differential Equations
AU  - Mohand M. Abdelrahim Mahgoub
AU  - Abdelbagy A. Alshikh
Y1  - 2017/01/18
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170501.12
DO  - 10.11648/j.ajam.20170501.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 14
EP  - 18
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170501.12
AB  - This paper aims to find analytical solutions of some analytical solutions of some non-linear differential equations using a new integral transform ''Aboodh transform'' with the differential transform method. The nonlinear terms can be easily handled by the use of differential transform method. This method is more efficient and easy to handle such differential equations in comparison to other methods. The results reveal that this method is very efficient, simple and can be applied to other nonlinear problems
VL  - 5
IS  - 1
ER  -

Copy | Download