Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions

Azhari Ahmad Abdalla

doi:doi:10.11648/j.mcs.20170201.11

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Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions

Azhari Ahmad Abdalla

Published in Mathematics and Computer Science (Volume 2, Issue 1)

Received: 21 November 2016 Accepted: 30 November 2016 Published: 3 January 2017

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Abstract

The main aim of this paper is to investigate the numerical solution of first kind integral equation of logarithmic kernel when using spectral method. Our approach consists of limiting the boundary to the unit interval and specify a logarithmic kernel. The behavior of the solution on the unit interval was analyzed and the advantages and disadvantages of this approach was shown.

Published in	Mathematics and Computer Science (Volume 2, Issue 1)
DOI	10.11648/j.mcs.20170201.11
Page(s)	1-5
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

Integral Equation, Spectral Method, Logarithmic Kernel

References

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[10]	E. S. Shoukralla, S. A. EL-Serafi and Nermein. Saber, “A Modified Iterative Method for the Solution of Fredholm Integral Equation of the Second Kind Via Matrices” International Journal of Universal Mathematics and Mathematical Sciences, 01 Issues No.: 02, ISSN No.: 2454-7271, Dec 2015.
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Azhari Ahmad Abdalla. (2017). Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions. Mathematics and Computer Science, 2(1), 1-5. https://doi.org/10.11648/j.mcs.20170201.11

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ACS Style

Azhari Ahmad Abdalla. Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions. Math. Comput. Sci. 2017, 2(1), 1-5. doi: 10.11648/j.mcs.20170201.11

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AMA Style

Azhari Ahmad Abdalla. Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions. Math Comput Sci. 2017;2(1):1-5. doi: 10.11648/j.mcs.20170201.11

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@article{10.11648/j.mcs.20170201.11,
  author = {Azhari Ahmad Abdalla},
  title = {Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions},
  journal = {Mathematics and Computer Science},
  volume = {2},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.mcs.20170201.11},
  url = {https://doi.org/10.11648/j.mcs.20170201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170201.11},
  abstract = {The main aim of this paper is to investigate the numerical solution of first kind integral equation of logarithmic kernel when using spectral method. Our approach consists of limiting the boundary to the unit interval and specify a logarithmic kernel. The behavior of the solution on the unit interval was analyzed and the advantages and disadvantages of this approach was shown.},
 year = {2017}
}

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TY  - JOUR
T1  - Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions
AU  - Azhari Ahmad Abdalla
Y1  - 2017/01/03
PY  - 2017
N1  - https://doi.org/10.11648/j.mcs.20170201.11
DO  - 10.11648/j.mcs.20170201.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20170201.11
AB  - The main aim of this paper is to investigate the numerical solution of first kind integral equation of logarithmic kernel when using spectral method. Our approach consists of limiting the boundary to the unit interval and specify a logarithmic kernel. The behavior of the solution on the unit interval was analyzed and the advantages and disadvantages of this approach was shown.
VL  - 2
IS  - 1
ER  -

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Author Information

Azhari Ahmad Abdalla

Department of Mathematics, University of Hail, Hail, Saudi Arabia

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APA Style

Azhari Ahmad Abdalla. (2017). Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions. Mathematics and Computer Science, 2(1), 1-5. https://doi.org/10.11648/j.mcs.20170201.11

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ACS Style

Azhari Ahmad Abdalla. Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions. Math. Comput. Sci. 2017, 2(1), 1-5. doi: 10.11648/j.mcs.20170201.11

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AMA Style

Azhari Ahmad Abdalla. Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions. Math Comput Sci. 2017;2(1):1-5. doi: 10.11648/j.mcs.20170201.11

Copy | Download

@article{10.11648/j.mcs.20170201.11,
  author = {Azhari Ahmad Abdalla},
  title = {Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions},
  journal = {Mathematics and Computer Science},
  volume = {2},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.mcs.20170201.11},
  url = {https://doi.org/10.11648/j.mcs.20170201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170201.11},
  abstract = {The main aim of this paper is to investigate the numerical solution of first kind integral equation of logarithmic kernel when using spectral method. Our approach consists of limiting the boundary to the unit interval and specify a logarithmic kernel. The behavior of the solution on the unit interval was analyzed and the advantages and disadvantages of this approach was shown.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions
AU  - Azhari Ahmad Abdalla
Y1  - 2017/01/03
PY  - 2017
N1  - https://doi.org/10.11648/j.mcs.20170201.11
DO  - 10.11648/j.mcs.20170201.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20170201.11
AB  - The main aim of this paper is to investigate the numerical solution of first kind integral equation of logarithmic kernel when using spectral method. Our approach consists of limiting the boundary to the unit interval and specify a logarithmic kernel. The behavior of the solution on the unit interval was analyzed and the advantages and disadvantages of this approach was shown.
VL  - 2
IS  - 1
ER  -

Copy | Download