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A Modified New Homotopy Perturbation Method for Solving Linear Integral Equations – Differential

Received: 11 May 2014     Accepted: 23 May 2014     Published: 10 June 2014
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Abstract

Mathematical modeling of real-life problems usually results in functional equations, such as ordinary or partial differential equations, integral and integral-differential equations etc. The theory of integral equation is one of the major topics of applied mathematics. In this paper a new Homotopy Perturbation Method (HPM) is introduced to obtain exact solutions of the systems of integral equations-differential and is provided examples for the accuracy of this method. This paper presents an introduction to new method of HPM, then introduces the system of integral - differential linear equations and also introduces applications and literature. In second section we will introduce categorizations of averaging integral - differential and several methods to solve this kind of achievement. The third section introduces a new method of HPM. Fourth section determines quarter of integral - differential equations by using HPM. Therefore, we provide Conclusion and some examples that illustrate the effectiveness and convenience of the proposed method.

Published in American Journal of Applied Mathematics (Volume 2, Issue 3)
DOI 10.11648/j.ajam.20140203.12
Page(s) 79-84
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), 2014. Published by Science Publishing Group

Keywords

New Homotopy Perturbation Method, Systems of Integral Equations - Differential

References
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Cite This Article
  • APA Style

    Aisan Khojasteh, Mahmoud Paripour. (2014). A Modified New Homotopy Perturbation Method for Solving Linear Integral Equations – Differential. American Journal of Applied Mathematics, 2(3), 79-84. https://doi.org/10.11648/j.ajam.20140203.12

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    ACS Style

    Aisan Khojasteh; Mahmoud Paripour. A Modified New Homotopy Perturbation Method for Solving Linear Integral Equations – Differential. Am. J. Appl. Math. 2014, 2(3), 79-84. doi: 10.11648/j.ajam.20140203.12

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    AMA Style

    Aisan Khojasteh, Mahmoud Paripour. A Modified New Homotopy Perturbation Method for Solving Linear Integral Equations – Differential. Am J Appl Math. 2014;2(3):79-84. doi: 10.11648/j.ajam.20140203.12

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  • @article{10.11648/j.ajam.20140203.12,
      author = {Aisan Khojasteh and Mahmoud Paripour},
      title = {A Modified New Homotopy Perturbation Method for Solving Linear Integral Equations – Differential},
      journal = {American Journal of Applied Mathematics},
      volume = {2},
      number = {3},
      pages = {79-84},
      doi = {10.11648/j.ajam.20140203.12},
      url = {https://doi.org/10.11648/j.ajam.20140203.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140203.12},
      abstract = {Mathematical modeling of real-life problems usually results in functional equations, such as ordinary or partial differential equations, integral and integral-differential equations etc. The theory of integral equation is one of the major topics of applied mathematics. In this paper a new Homotopy Perturbation Method (HPM) is introduced to obtain exact solutions of the systems of integral equations-differential and is provided examples for the accuracy of this method. This paper presents an introduction to new method of HPM, then introduces the system of integral - differential linear equations and also introduces applications and literature. In second section we will introduce categorizations of averaging integral - differential and several methods to solve this kind of achievement. The third section introduces a new method of HPM. Fourth section determines quarter of integral - differential equations by using HPM. Therefore, we provide Conclusion and some examples that illustrate the effectiveness and convenience of the proposed method.},
     year = {2014}
    }
    

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    T1  - A Modified New Homotopy Perturbation Method for Solving Linear Integral Equations – Differential
    AU  - Aisan Khojasteh
    AU  - Mahmoud Paripour
    Y1  - 2014/06/10
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ajam.20140203.12
    DO  - 10.11648/j.ajam.20140203.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 79
    EP  - 84
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20140203.12
    AB  - Mathematical modeling of real-life problems usually results in functional equations, such as ordinary or partial differential equations, integral and integral-differential equations etc. The theory of integral equation is one of the major topics of applied mathematics. In this paper a new Homotopy Perturbation Method (HPM) is introduced to obtain exact solutions of the systems of integral equations-differential and is provided examples for the accuracy of this method. This paper presents an introduction to new method of HPM, then introduces the system of integral - differential linear equations and also introduces applications and literature. In second section we will introduce categorizations of averaging integral - differential and several methods to solve this kind of achievement. The third section introduces a new method of HPM. Fourth section determines quarter of integral - differential equations by using HPM. Therefore, we provide Conclusion and some examples that illustrate the effectiveness and convenience of the proposed method.
    VL  - 2
    IS  - 3
    ER  - 

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Author Information
  • M. A. Applied Mathematics, Science and Research Branch, Islamic Azad University, Broujerd, Iran

  • Assistant Professor of Applied Mathematics, Hamedan University of Technology, Hamedan, Iran

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