Applied and Computational Mathematics

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A New Straightforward Method for Evaluating Singular Integrals

Received: 27 May 2015    Accepted: 3 June 2015    Published: 13 October 2015
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Abstract

A new more accurate straightforward method is presented for evaluating the singular integrals. A few methods in numerical analysis is useful for evaluating the integral where singularities arises, most of them uses extrapolation technique at singular point. This new method uses directly and gives better results and the Romberg integration of this formula converses faster than others previous methods.

DOI 10.11648/j.acm.20150406.14
Published in Applied and Computational Mathematics (Volume 4, Issue 6, December 2015)
Page(s) 420-423
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

Numerical Integration, Singular Integrals, Lagrange’s Interpolation Formula, Romberg Integration

References
[1] L. Fox, Romberg integration for a class of singular integrand, Computer. Journal. 10(1) (1967), pp87-93.
[2] M. A. Huq, M. K. Hasan, M. M. Rahman and M. S. Alam, A Simple and Straightforward Method for evaluating some singular integrals, Far East Journal of Mathematical Education V-7, N-2, 2011, pp 93-103.
[3] E. A. Alshina, N. N. Kalitkin, I. A. Panin and I. P. Poshivaiol, Numerical integration of functions with singularities, Doki. Math. 74(2) (2006), pp 771-774.
[4] Numerical Mathematical Analysis, By James Blaine Scarborough, Publisher: Johns Hopkins Press, 1966ISBN0801805759, 9780801805752.
[5] Introductory Methods of Numerical Analysis, By S. S. Sastry, Prentice-Hall on India, New Delhi. ISBN: 8120327616, 9788120327610.
[6] L. M. Delves, The numerical evaluation of principal value integrals, Comput. J. 10(4) (1968), pp 389-391.
[7] B. D. Hunter, The numerical evaluation of Cauchy principal values of integrals by Romberg integration, Numer. Math. 21(3) (1973) pp 185-192.
[8] H. W Stolle and R. Strauss, “On the Numerical Integration of Certain Singular Integrals”, Computing, Vol. 48(2), (1992), pp177-189.
[9] Linz, P. “On the approximate computation of certain strongly singular integrals.” Computing35, 345–353 (1985).
[10] D. F. Paget, “The numerical evaluation of Hadamard finite-part integrals”, Numerische Mathematik, Volume 36, Issue 4, pp 447-453, (1981).
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  • APA Style

    Md. Habibur Rahaman, Md. Ashraful Huq, M. Kamrul Hasan. (2015). A New Straightforward Method for Evaluating Singular Integrals. Applied and Computational Mathematics, 4(6), 420-423. https://doi.org/10.11648/j.acm.20150406.14

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    ACS Style

    Md. Habibur Rahaman; Md. Ashraful Huq; M. Kamrul Hasan. A New Straightforward Method for Evaluating Singular Integrals. Appl. Comput. Math. 2015, 4(6), 420-423. doi: 10.11648/j.acm.20150406.14

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    AMA Style

    Md. Habibur Rahaman, Md. Ashraful Huq, M. Kamrul Hasan. A New Straightforward Method for Evaluating Singular Integrals. Appl Comput Math. 2015;4(6):420-423. doi: 10.11648/j.acm.20150406.14

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  • @article{10.11648/j.acm.20150406.14,
      author = {Md. Habibur Rahaman and Md. Ashraful Huq and M. Kamrul Hasan},
      title = {A New Straightforward Method for Evaluating Singular Integrals},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {6},
      pages = {420-423},
      doi = {10.11648/j.acm.20150406.14},
      url = {https://doi.org/10.11648/j.acm.20150406.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150406.14},
      abstract = {A new more accurate straightforward method is presented for evaluating the singular integrals. A few methods in numerical analysis is useful for evaluating the integral where singularities arises, most of them uses extrapolation technique at singular point. This new method uses directly and gives better results and the Romberg integration of this formula converses faster than others previous methods.},
     year = {2015}
    }
    

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Author Information
  • Department of Mathematics, Rajshahi University of Engineering and Technology, Kazla, Rajshahi-6204, Bangladesh; Adarsho Karigori & Banijjik College, Hatemkhan, Rajshahi-6000, Bangladesh

  • Department of Mathematics, Rajshahi University of Engineering and Technology, Kazla, Rajshahi-6204, Bangladesh

  • Department of Mathematics, Rajshahi University of Engineering and Technology, Kazla, Rajshahi-6204, Bangladesh

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