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RBFs for Integral Equations with a Weakly Singular Kernel

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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  • APA Style

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

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

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