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

Aisan Khojasteh; Mahmoud Paripour

doi:doi:10.11648/j.ajam.20140203.12

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

Aisan Khojasteh, Mahmoud Paripour

Published in American Journal of Applied Mathematics (Volume 2, Issue 3)

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), 2024. Published by Science Publishing Group

Keywords

New Homotopy Perturbation Method, Systems of Integral Equations - Differential

References

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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://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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TY  - JOUR
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

Aisan Khojasteh

M. A. Applied Mathematics, Science and Research Branch, Islamic Azad University, Broujerd, Iran
Mahmoud Paripour

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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  -

Copy | Download