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Approximate Solutions for Mathematical Model of Carcinogenesis Using Adomian Decomposition Method

Received: 20 March 2017     Accepted: 21 March 2017     Published: 5 April 2017
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Abstract

In this paper, the Adomian decomposition method (ADM) is applied to obtain the approximate solution of a mathematical model of carcinogenesis which is a Riccati differential equation derived by Moolgavkar and Venzon (see [9]). The numerical solution obtained by this way have been compared with the exact solution which obtained by Moolgavkar and Venzon (see [11]). This comparison show that the (ADM) is a powerful method for solving this differential equations. The method does not need weak nonlinearity assumptions or perturbation theory, the decomposition procedure of Adomian will be obtained easily without linearization the problem by implementing the decomposition method rather than the standard methods for the exact solutions.

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5-1)

This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics

DOI 10.11648/j.ajtas.s.2017060501.16
Page(s) 40-45
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

Adomian Decomposition Method, Riccati Differential Equation, Carcinogenesis, Error Absolute

References
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  • APA Style

    Mahmoud M. El-borai, M. A. Abdou, E. M. Youssef. (2017). Approximate Solutions for Mathematical Model of Carcinogenesis Using Adomian Decomposition Method. American Journal of Theoretical and Applied Statistics, 6(5-1), 40-45. https://doi.org/10.11648/j.ajtas.s.2017060501.16

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    ACS Style

    Mahmoud M. El-borai; M. A. Abdou; E. M. Youssef. Approximate Solutions for Mathematical Model of Carcinogenesis Using Adomian Decomposition Method. Am. J. Theor. Appl. Stat. 2017, 6(5-1), 40-45. doi: 10.11648/j.ajtas.s.2017060501.16

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    AMA Style

    Mahmoud M. El-borai, M. A. Abdou, E. M. Youssef. Approximate Solutions for Mathematical Model of Carcinogenesis Using Adomian Decomposition Method. Am J Theor Appl Stat. 2017;6(5-1):40-45. doi: 10.11648/j.ajtas.s.2017060501.16

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  • @article{10.11648/j.ajtas.s.2017060501.16,
      author = {Mahmoud M. El-borai and M. A. Abdou and E. M. Youssef},
      title = {Approximate Solutions for Mathematical Model of Carcinogenesis Using Adomian Decomposition Method},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {5-1},
      pages = {40-45},
      doi = {10.11648/j.ajtas.s.2017060501.16},
      url = {https://doi.org/10.11648/j.ajtas.s.2017060501.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2017060501.16},
      abstract = {In this paper, the Adomian decomposition method (ADM) is applied to obtain the approximate solution of a mathematical model of carcinogenesis which is a Riccati differential equation derived by Moolgavkar and Venzon (see [9]). The numerical solution obtained by this way have been compared with the exact solution which obtained by Moolgavkar and Venzon (see [11]). This comparison show that the (ADM) is a powerful method for solving this differential equations. The method does not need weak nonlinearity assumptions or perturbation theory, the decomposition procedure of Adomian will be obtained easily without linearization the problem by implementing the decomposition method rather than the standard methods for the exact solutions.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Approximate Solutions for Mathematical Model of Carcinogenesis Using Adomian Decomposition Method
    AU  - Mahmoud M. El-borai
    AU  - M. A. Abdou
    AU  - E. M. Youssef
    Y1  - 2017/04/05
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajtas.s.2017060501.16
    DO  - 10.11648/j.ajtas.s.2017060501.16
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 40
    EP  - 45
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.s.2017060501.16
    AB  - In this paper, the Adomian decomposition method (ADM) is applied to obtain the approximate solution of a mathematical model of carcinogenesis which is a Riccati differential equation derived by Moolgavkar and Venzon (see [9]). The numerical solution obtained by this way have been compared with the exact solution which obtained by Moolgavkar and Venzon (see [11]). This comparison show that the (ADM) is a powerful method for solving this differential equations. The method does not need weak nonlinearity assumptions or perturbation theory, the decomposition procedure of Adomian will be obtained easily without linearization the problem by implementing the decomposition method rather than the standard methods for the exact solutions.
    VL  - 6
    IS  - 5-1
    ER  - 

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Author Information
  • Faculty of Science, Alexandria University, Alexandria, Egypt

  • Faculty of Education, Alexandria University, Alexandria, Egypt

  • Faculty of Education, Alexandria University, Alexandria, Egypt

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