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Ramadan Group (RG) Transform Coupled with Projected Differential Transform for Solving Nonlinear Partial Differential Equations

Received: 7 January 2017     Accepted: 20 January 2017     Published: 21 February 2017
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Abstract

In this article a combination of integral transform method (Ramadan group transform) and projected differential transform is considered to solve partial differential equations. The method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work. The fact that the suggested hybrid method solves such nonlinear partial differential equations without using He’s polynomials or Adomian’s polynomials is a clear advantage over these decomposition methods. Numerical examples are performed by this hybrid method are presented. The results reveal that the suggested method is simple and effective.

Published in American Journal of Mathematical and Computer Modelling (Volume 2, Issue 2)
DOI 10.11648/j.ajmcm.20170202.11
Page(s) 39-47
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

Integral Transform Method, Projected Differential Transform Method, He Polynomials, Adomian Polynomials, Partial Differential Equations

References
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[2] S. Weerakoon, Application of Sumudu transform to partial differential equations, International Journal of Mathematical Education in Science and Technology, Vol. 25, No. 2, pp. 277-283, 1994.
[3] S. Weerakoon, Complex inversion formula for Sumudu transform, International Journal of Mathematical Education in Science and Technology, Vol. 29, No. 4, pp. 618-621, 1998.
[4] M. A. Asiru, "Further properties of the Sumudu transform and its applications", International Journal of Mathematical Education in Science and Technology, Vol. 33, No. 3, pp. 441-449, 2002.
[5] A. Kadem, "Solving the one-dimensional neutron transport equation using Chebyshev polynomials and the Sumudu transform", Analele Universitatii dinOradea, Vol. 12, pp. 153-171, 2005.
[6] A. Kilicman, H. Eltayeb, and K. A. M. Atan, "A note on the comparison between Laplace and Sumudu transforms", Iranian Mathematical Society, Vol. 37, No. 1, pp. 131-141, 2011.
[7] A. Kilicman and H. E. Gadain, "On the applications of Laplace and Sumudu transforms" Journal of the Franklin Institute, Vol. 347, No. 5, pp. 848-862, 2010.
[8] H. Eltayeb, A. Kilicman, and B. Fisher, "A new integral transform and associated distributions", Integral Transforms and Special Functions, Vol. 21, No. 5-6, pp. 367- 379, 2010.
[9] A. Kilicman and H. Eltayeb, "A note on integral transforms and partial differential equations", Applied Mathematical Sciences, Vol. 4, No. 1-4, pp. 109-118, 2010.
[10] A. Kilicman, H. Eltayeb, and R. P. Agarwal, "On Sumudu transform and system of differential equations", Abstract and Applied Analysis, Article ID 598702, 11 pages, 2010.
[11] J. Zhang, "A Sumudu based algorithm for solving differential equations", Academy of Sciences of Moldova, Vol. 15, No. 3, pp. 303-313, 2007.
[12] Kamal. R. Raslan, Mohamed A. Ramadan, Talaat S. EL-Danaf, and Adel R. Hadhoud, On a New General Integral Transform: Some Properties and Remarks, Journal of Mathematical and Computational Science, 6 (1), 103-109, 2016.
[13] Z. H. Khan and W. A. Khan, N-Transform – Properties and Application, NUST Journal of Engineering Sciences, Vol. 1, No., 127-133, 2008.
[14] Mohamed A. Ramadan and Mohamed. S. Al-luhaibi” New Iterative Method Solving the Fornberg- Whitham Equation and Comparison with Homotopy Perturbation Transform Method” British Journal of Mathematics & Computer Science 4 (9): 1213-1227, 2014.
[15] Mohamed A. Ramadan, Mohamed. S. Al-luhaibi “Application of Sumudu decomposition method for Solving Linear and Nonlinear Klein-Gordon Equations” International Journal of Soft Computing and Engineering, (IJSCE) ISSN: 2231- 2307, Volume-3, Issue-6, January 2014.
[16] Mohamed A. Ramadan and Mohamed. S. Al-luhaibi” Application of Sumudu decomposition method for solving nonlinear Wave-like equations with variable coefficients, Electronic Journal of Mathematical Analysis and Applications (EJMAA) Vol. 4 (1) pp. 116-124, Jan., 2016.
[17] T. M. Elzaki, Application of Projected Differential Transform Method on Nonlinear Partial Differential Equations with Proportional Delay in One Variable, World Applied Sciences Journal, 30, 345-349, 2014.
[18] Y. Do and B. Jang, Nonlinear Klein – Gordon and Schrödinger Equations by the Projected Differential Transform Method, Abstract and Applied Analysis, Vol. 2012, Article ID 150527, 15 pages.
Cite This Article
  • APA Style

    Mohamed A. Ramadan, Adel R. Hadhoud. (2017). Ramadan Group (RG) Transform Coupled with Projected Differential Transform for Solving Nonlinear Partial Differential Equations. American Journal of Mathematical and Computer Modelling, 2(2), 39-47. https://doi.org/10.11648/j.ajmcm.20170202.11

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    ACS Style

    Mohamed A. Ramadan; Adel R. Hadhoud. Ramadan Group (RG) Transform Coupled with Projected Differential Transform for Solving Nonlinear Partial Differential Equations. Am. J. Math. Comput. Model. 2017, 2(2), 39-47. doi: 10.11648/j.ajmcm.20170202.11

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    AMA Style

    Mohamed A. Ramadan, Adel R. Hadhoud. Ramadan Group (RG) Transform Coupled with Projected Differential Transform for Solving Nonlinear Partial Differential Equations. Am J Math Comput Model. 2017;2(2):39-47. doi: 10.11648/j.ajmcm.20170202.11

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  • @article{10.11648/j.ajmcm.20170202.11,
      author = {Mohamed A. Ramadan and Adel R. Hadhoud},
      title = {Ramadan Group (RG) Transform Coupled with Projected Differential Transform for Solving Nonlinear Partial Differential Equations},
      journal = {American Journal of Mathematical and Computer Modelling},
      volume = {2},
      number = {2},
      pages = {39-47},
      doi = {10.11648/j.ajmcm.20170202.11},
      url = {https://doi.org/10.11648/j.ajmcm.20170202.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20170202.11},
      abstract = {In this article a combination of integral transform method (Ramadan group transform) and projected differential transform is considered to solve partial differential equations. The method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work. The fact that the suggested hybrid method solves such nonlinear partial differential equations without using He’s polynomials or Adomian’s polynomials is a clear advantage over these decomposition methods. Numerical examples are performed by this hybrid method are presented. The results reveal that the suggested method is simple and effective.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Ramadan Group (RG) Transform Coupled with Projected Differential Transform for Solving Nonlinear Partial Differential Equations
    AU  - Mohamed A. Ramadan
    AU  - Adel R. Hadhoud
    Y1  - 2017/02/21
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    DO  - 10.11648/j.ajmcm.20170202.11
    T2  - American Journal of Mathematical and Computer Modelling
    JF  - American Journal of Mathematical and Computer Modelling
    JO  - American Journal of Mathematical and Computer Modelling
    SP  - 39
    EP  - 47
    PB  - Science Publishing Group
    SN  - 2578-8280
    UR  - https://doi.org/10.11648/j.ajmcm.20170202.11
    AB  - In this article a combination of integral transform method (Ramadan group transform) and projected differential transform is considered to solve partial differential equations. The method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work. The fact that the suggested hybrid method solves such nonlinear partial differential equations without using He’s polynomials or Adomian’s polynomials is a clear advantage over these decomposition methods. Numerical examples are performed by this hybrid method are presented. The results reveal that the suggested method is simple and effective.
    VL  - 2
    IS  - 2
    ER  - 

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Author Information
  • Mathematics Department, Faculty of Science, Menoufia University, Shebeen El-Koom, Egypt

  • Mathematics Department, Faculty of Science, Menoufia University, Shebeen El-Koom, Egypt

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