American Journal of Applied Mathematics

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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.

DOI 10.11648/j.ajam.20140203.12
Published in American Journal of Applied Mathematics (Volume 2, Issue 3, June 2014)
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), 2024. Published by Science Publishing Group

Keywords

New Homotopy Perturbation Method, Systems of Integral Equations - Differential

References
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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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  • 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://download.sciencepg.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
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    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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