Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind

Salam Jasim Majeed

doi:doi:10.11648/j.ajam.20140205.12

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Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind

Salam Jasim Majeed

Published in American Journal of Applied Mathematics (Volume 2, Issue 5)

Received: 24 August 2014 Accepted: 6 September 2014 Published: 30 September 2014

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Abstract

In this paper numerical solution to system of linear Fredholm integral equations by modified midpoint method is considered. This method transforms the system of linear Fredholm integral equations into a system of linear algebraic equations that can be solved easily with any of the usual methods. Finally, some illustrative examples are presented to test this method and the results reveal that this method is very effective and convenient by comparison with exact solution and with other numerical methods such as midpoint method, trapezoidal method, Simpson's method and modified trapezoidal method. All results are computed by using a programs written in Matlab R2012b.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 5)
DOI	10.11648/j.ajam.20140205.12
Page(s)	155-161
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

System of Fredholm Integral Equations, Modified Midpoint Method

References

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[17]	S. J. Majeed, ‘‘Modified Midpoint Method For Solving Linear Fredholm Integral Equations Of The Second Kind ", J. Al Qadisiya for computers Science and mathematics, Vol.3 (1), 2011, pp.28-46.
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Salam Jasim Majeed. (2014). Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind. American Journal of Applied Mathematics, 2(5), 155-161. https://doi.org/10.11648/j.ajam.20140205.12

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Salam Jasim Majeed. Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind. Am. J. Appl. Math. 2014, 2(5), 155-161. doi: 10.11648/j.ajam.20140205.12

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AMA Style

Salam Jasim Majeed. Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind. Am J Appl Math. 2014;2(5):155-161. doi: 10.11648/j.ajam.20140205.12

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@article{10.11648/j.ajam.20140205.12,
  author = {Salam Jasim Majeed},
  title = {Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {5},
  pages = {155-161},
  doi = {10.11648/j.ajam.20140205.12},
  url = {https://doi.org/10.11648/j.ajam.20140205.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140205.12},
  abstract = {In this paper numerical solution to system of linear Fredholm integral equations by modified midpoint method is considered. This method transforms the system of linear Fredholm integral equations into a system of linear algebraic equations that can be solved easily with any of the usual methods. Finally, some illustrative examples are presented to test this method and the results reveal that this method is very effective and convenient by comparison with exact solution and with other numerical methods such as midpoint method, trapezoidal method, Simpson's method and modified trapezoidal method. All results are computed by using a programs written in Matlab R2012b.},
 year = {2014}
}

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TY  - JOUR
T1  - Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind
AU  - Salam Jasim Majeed
Y1  - 2014/09/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140205.12
DO  - 10.11648/j.ajam.20140205.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 155
EP  - 161
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140205.12
AB  - In this paper numerical solution to system of linear Fredholm integral equations by modified midpoint method is considered. This method transforms the system of linear Fredholm integral equations into a system of linear algebraic equations that can be solved easily with any of the usual methods. Finally, some illustrative examples are presented to test this method and the results reveal that this method is very effective and convenient by comparison with exact solution and with other numerical methods such as midpoint method, trapezoidal method, Simpson's method and modified trapezoidal method. All results are computed by using a programs written in Matlab R2012b.
VL  - 2
IS  - 5
ER  -

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Author Information

Salam Jasim Majeed

Department of Physics, College of Science, University of Thi-Qar, Thi-Qar, Iraq

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Salam Jasim Majeed. (2014). Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind. American Journal of Applied Mathematics, 2(5), 155-161. https://doi.org/10.11648/j.ajam.20140205.12

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ACS Style

Salam Jasim Majeed. Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind. Am. J. Appl. Math. 2014, 2(5), 155-161. doi: 10.11648/j.ajam.20140205.12

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AMA Style

Salam Jasim Majeed. Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind. Am J Appl Math. 2014;2(5):155-161. doi: 10.11648/j.ajam.20140205.12

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@article{10.11648/j.ajam.20140205.12,
  author = {Salam Jasim Majeed},
  title = {Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {5},
  pages = {155-161},
  doi = {10.11648/j.ajam.20140205.12},
  url = {https://doi.org/10.11648/j.ajam.20140205.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140205.12},
  abstract = {In this paper numerical solution to system of linear Fredholm integral equations by modified midpoint method is considered. This method transforms the system of linear Fredholm integral equations into a system of linear algebraic equations that can be solved easily with any of the usual methods. Finally, some illustrative examples are presented to test this method and the results reveal that this method is very effective and convenient by comparison with exact solution and with other numerical methods such as midpoint method, trapezoidal method, Simpson's method and modified trapezoidal method. All results are computed by using a programs written in Matlab R2012b.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind
AU  - Salam Jasim Majeed
Y1  - 2014/09/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140205.12
DO  - 10.11648/j.ajam.20140205.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 155
EP  - 161
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140205.12
AB  - In this paper numerical solution to system of linear Fredholm integral equations by modified midpoint method is considered. This method transforms the system of linear Fredholm integral equations into a system of linear algebraic equations that can be solved easily with any of the usual methods. Finally, some illustrative examples are presented to test this method and the results reveal that this method is very effective and convenient by comparison with exact solution and with other numerical methods such as midpoint method, trapezoidal method, Simpson's method and modified trapezoidal method. All results are computed by using a programs written in Matlab R2012b.
VL  - 2
IS  - 5
ER  -

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