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FD-RBF for Partial Integro-Differential Equations with a Weakly Singular Kernel

Received: 25 September 2015     Accepted: 7 October 2015     Published: 23 October 2015
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Abstract

Finite Difference Method and Radial Basis Functions are applied to solve partial integro-differential equations with a weakly singular kernel. The product trapezoidal method is used to compute singular integrals that appear in the discretization process. Different RBFs are implemented and satisfactory results are shown the ability and the usefulness of the proposed method.

Published in Applied and Computational Mathematics (Volume 4, Issue 6)
DOI 10.11648/j.acm.20150406.17
Page(s) 445-451
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

Partial Integro-Differential Equations (PIDE), Weakly Singular Kernel, Radial Basis Functions (RBF), Finite Difference Method (FDM), Product Trapezoidal Method

References
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Cite This Article
  • APA Style

    Jafar Biazar, Mohammad Ali Asadi. (2015). FD-RBF for Partial Integro-Differential Equations with a Weakly Singular Kernel. Applied and Computational Mathematics, 4(6), 445-451. https://doi.org/10.11648/j.acm.20150406.17

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    ACS Style

    Jafar Biazar; Mohammad Ali Asadi. FD-RBF for Partial Integro-Differential Equations with a Weakly Singular Kernel. Appl. Comput. Math. 2015, 4(6), 445-451. doi: 10.11648/j.acm.20150406.17

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    AMA Style

    Jafar Biazar, Mohammad Ali Asadi. FD-RBF for Partial Integro-Differential Equations with a Weakly Singular Kernel. Appl Comput Math. 2015;4(6):445-451. doi: 10.11648/j.acm.20150406.17

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  • @article{10.11648/j.acm.20150406.17,
      author = {Jafar Biazar and Mohammad Ali Asadi},
      title = {FD-RBF for Partial Integro-Differential Equations with a Weakly Singular Kernel},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {6},
      pages = {445-451},
      doi = {10.11648/j.acm.20150406.17},
      url = {https://doi.org/10.11648/j.acm.20150406.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150406.17},
      abstract = {Finite Difference Method and Radial Basis Functions are applied to solve partial integro-differential equations with a weakly singular kernel. The product trapezoidal method is used to compute singular integrals that appear in the discretization process. Different RBFs are implemented and satisfactory results are shown the ability and the usefulness of the proposed method.},
     year = {2015}
    }
    

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    AU  - Jafar Biazar
    AU  - Mohammad Ali Asadi
    Y1  - 2015/10/23
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    N1  - https://doi.org/10.11648/j.acm.20150406.17
    DO  - 10.11648/j.acm.20150406.17
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    AB  - Finite Difference Method and Radial Basis Functions are applied to solve partial integro-differential equations with a weakly singular kernel. The product trapezoidal method is used to compute singular integrals that appear in the discretization process. Different RBFs are implemented and satisfactory results are shown the ability and the usefulness of the proposed method.
    VL  - 4
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    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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