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Numerical KDV Equation by the Adomian Decomposition Method

Received: 17 March 2013     Published: 2 May 2013
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Abstract

Using the Adomian decomposition method (ADM), we present in this paper a numerical approximation of the solution of the nonlinear KDV equation. The principal task concerns essentially the computation of the Adomian polynomials for this type of equation and thereafter determining a significant criterion to ensure the conditions for convergence of the method.

Published in American Journal of Modern Physics (Volume 2, Issue 3)
DOI 10.11648/j.ajmp.20130203.13
Page(s) 111-115
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), 2013. Published by Science Publishing Group

Keywords

KDV Equation, Numerical Approach, Adomian Decomposition

References
[1] K. Abbaoui and Y. Cherruault, Convergence of adomian’s method applied to differential equations, Comp Math Appl (1994).
[2] K. Abbaoui and Y. Cherruault, Convergence of Adomian’s method applied to nonlinear equations, Math Computer Model (1994).
[3] N. Himoun, K. Abbaoui, and Y. Cherruault, New results of convergence of Adomian’s method, Kybernetes (1999).
[4] Y. Zhu, Q. Chang, and S. Wu, A new algorithm for calculating Adomian polynomials, Appl. Math. Comput. (2005).
[5] M. Inc, On numerical solution of partial differential equation by the decomposition method, Kragujevac J Math (2004).
Cite This Article
  • APA Style

    M. Akdi, M. B. Sedra. (2013). Numerical KDV Equation by the Adomian Decomposition Method. American Journal of Modern Physics, 2(3), 111-115. https://doi.org/10.11648/j.ajmp.20130203.13

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    ACS Style

    M. Akdi; M. B. Sedra. Numerical KDV Equation by the Adomian Decomposition Method. Am. J. Mod. Phys. 2013, 2(3), 111-115. doi: 10.11648/j.ajmp.20130203.13

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    AMA Style

    M. Akdi, M. B. Sedra. Numerical KDV Equation by the Adomian Decomposition Method. Am J Mod Phys. 2013;2(3):111-115. doi: 10.11648/j.ajmp.20130203.13

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  • @article{10.11648/j.ajmp.20130203.13,
      author = {M. Akdi and M. B. Sedra},
      title = {Numerical KDV Equation by the Adomian Decomposition Method},
      journal = {American Journal of Modern Physics},
      volume = {2},
      number = {3},
      pages = {111-115},
      doi = {10.11648/j.ajmp.20130203.13},
      url = {https://doi.org/10.11648/j.ajmp.20130203.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20130203.13},
      abstract = {Using the Adomian decomposition method (ADM), we present in this paper a numerical approximation of the solution of the nonlinear KDV equation. The principal task concerns essentially the computation of the Adomian polynomials for this type of equation and thereafter determining a significant criterion to ensure the conditions for convergence of the method.},
     year = {2013}
    }
    

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  • TY  - JOUR
    T1  - Numerical KDV Equation by the Adomian Decomposition Method
    AU  - M. Akdi
    AU  - M. B. Sedra
    Y1  - 2013/05/02
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    N1  - https://doi.org/10.11648/j.ajmp.20130203.13
    DO  - 10.11648/j.ajmp.20130203.13
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 111
    EP  - 115
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20130203.13
    AB  - Using the Adomian decomposition method (ADM), we present in this paper a numerical approximation of the solution of the nonlinear KDV equation. The principal task concerns essentially the computation of the Adomian polynomials for this type of equation and thereafter determining a significant criterion to ensure the conditions for convergence of the method.
    VL  - 2
    IS  - 3
    ER  - 

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Author Information
  • Université Ibn Tofail, Faculté des Sciences, Département de Physique, LHESIR, Kénitra, Morocco

  • Université Ibn Tofail, Faculté des Sciences, Département de Physique, LHESIR, Kénitra, Morocco

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