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Application of the Differential Transform Method for the Nonlinear Differential Equations

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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[6] J. S. Duan, R. Rach, D. Buleanu, and A. M. Wazwaz, “A review of the Adomian decomposition method and its applications to fractional differential equations,” Communications in FractionalCalculus, vol. 3, no. 2, (2012). pp. 73-99.
[7] Bhaben Ch. Neog, Solutions of some system of non-linear PDEs using Reduced Differential Transform Method, IOSR Journal of Mathematics (IOSR-JM), Volume 11, Issue 5 Ver. I (Sep. - Oct. 2015), PP 37-44.
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[10] C. K. Chen, Solving partial differential equations by two dimensional differential transform, Appl. Math. Comput. 106 (1999) 171-179.
[11] H. Guoqiang, W. Jiong, Extrapolation of nystrom solution for two dimensional nonlinear Fredholm integral equations, J. Comput. Appl. Math. 134 (2001) 259-268.
[12] H. Guoqiang, W. Ruifang, Richardson extrapolation of iterated discrete Galerkin solution for two dimensional nonlinear Fredholm integral equations, J. Comput. Appl. Math. 139 (2002) 49-63.
[13] M. J. Jang, C. K. Chen, Y. C. Liu, Two-dimensional differential transform for partial differential equations, Appl. Math. Comput. 121 (2001) 261-270.
[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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  • APA Style

    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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    AU  - Abdelbagy A. Alshikh
    Y1  - 2017/01/18
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    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    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
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Author Information
  • Department of Mathematics, Faculty of Science & Technology, Omdurman Islamic University, Khartoum, Sudan

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

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