RBFs for Integral Equations with a Weakly Singular Kernel

Jafar Biazar; Mohammad Ali Asadi

doi:doi:10.11648/j.ajam.20150306.12

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RBFs for Integral Equations with a Weakly Singular Kernel

Jafar Biazar, Mohammad Ali Asadi

Published in American Journal of Applied Mathematics (Volume 3, Issue 6)

Received: 29 September 2015 Accepted: 9 October 2015 Published: 21 October 2015

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Abstract

In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. In addition, the results of applying the method are compared with those of Homotopy perturbation, and Adomian decomposition methods.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.ajam.20150306.12
Page(s)	250-255
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), 2015. Published by Science Publishing Group

Keywords

Integral Equations with a Weakly Singular Kernels, Radial Basis Functions (RBF), Adaptive Lobatto Quadrature, Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM)

References

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Jafar Biazar, Mohammad Ali Asadi. (2015). RBFs for Integral Equations with a Weakly Singular Kernel. American Journal of Applied Mathematics, 3(6), 250-255. https://doi.org/10.11648/j.ajam.20150306.12

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ACS Style

Jafar Biazar; Mohammad Ali Asadi. RBFs for Integral Equations with a Weakly Singular Kernel. Am. J. Appl. Math. 2015, 3(6), 250-255. doi: 10.11648/j.ajam.20150306.12

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AMA Style

Jafar Biazar, Mohammad Ali Asadi. RBFs for Integral Equations with a Weakly Singular Kernel. Am J Appl Math. 2015;3(6):250-255. doi: 10.11648/j.ajam.20150306.12

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@article{10.11648/j.ajam.20150306.12,
  author = {Jafar Biazar and Mohammad Ali Asadi},
  title = {RBFs for Integral Equations with a Weakly Singular Kernel},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {250-255},
  doi = {10.11648/j.ajam.20150306.12},
  url = {https://doi.org/10.11648/j.ajam.20150306.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.12},
  abstract = {In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. In addition, the results of applying the method are compared with those of Homotopy perturbation, and Adomian decomposition methods.},
 year = {2015}
}

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TY  - JOUR
T1  - RBFs for Integral Equations with a Weakly Singular Kernel
AU  - Jafar Biazar
AU  - Mohammad Ali Asadi
Y1  - 2015/10/21
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150306.12
DO  - 10.11648/j.ajam.20150306.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 250
EP  - 255
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150306.12
AB  - In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. In addition, the results of applying the method are compared with those of Homotopy perturbation, and Adomian decomposition methods.
VL  - 3
IS  - 6
ER  -

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Author Information

Jafar Biazar

Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran
Mohammad Ali Asadi

Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran

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Jafar Biazar, Mohammad Ali Asadi. (2015). RBFs for Integral Equations with a Weakly Singular Kernel. American Journal of Applied Mathematics, 3(6), 250-255. https://doi.org/10.11648/j.ajam.20150306.12

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ACS Style

Jafar Biazar; Mohammad Ali Asadi. RBFs for Integral Equations with a Weakly Singular Kernel. Am. J. Appl. Math. 2015, 3(6), 250-255. doi: 10.11648/j.ajam.20150306.12

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AMA Style

Jafar Biazar, Mohammad Ali Asadi. RBFs for Integral Equations with a Weakly Singular Kernel. Am J Appl Math. 2015;3(6):250-255. doi: 10.11648/j.ajam.20150306.12

Copy | Download

@article{10.11648/j.ajam.20150306.12,
  author = {Jafar Biazar and Mohammad Ali Asadi},
  title = {RBFs for Integral Equations with a Weakly Singular Kernel},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {250-255},
  doi = {10.11648/j.ajam.20150306.12},
  url = {https://doi.org/10.11648/j.ajam.20150306.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.12},
  abstract = {In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. In addition, the results of applying the method are compared with those of Homotopy perturbation, and Adomian decomposition methods.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - RBFs for Integral Equations with a Weakly Singular Kernel
AU  - Jafar Biazar
AU  - Mohammad Ali Asadi
Y1  - 2015/10/21
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150306.12
DO  - 10.11648/j.ajam.20150306.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 250
EP  - 255
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150306.12
AB  - In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. In addition, the results of applying the method are compared with those of Homotopy perturbation, and Adomian decomposition methods.
VL  - 3
IS  - 6
ER  -

Copy | Download