A New Straightforward Method for Evaluating Singular Integrals

Md. Habibur Rahaman; Md. Ashraful Huq; M. Kamrul Hasan

doi:doi:10.11648/j.acm.20150406.14

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A New Straightforward Method for Evaluating Singular Integrals

Md. Habibur Rahaman, Md. Ashraful Huq, M. Kamrul Hasan

Published in Applied and Computational Mathematics (Volume 4, Issue 6)

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.

Published in	Applied and Computational Mathematics (Volume 4, Issue 6)
DOI	10.11648/j.acm.20150406.14
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), 2015. 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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TY  - JOUR
T1  - A New Straightforward Method for Evaluating Singular Integrals
AU  - Md. Habibur Rahaman
AU  - Md. Ashraful Huq
AU  - M. Kamrul Hasan
Y1  - 2015/10/13
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AB  - 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.
VL  - 4
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Author Information

Md. Habibur Rahaman

Department of Mathematics, Rajshahi University of Engineering and Technology, Kazla, Rajshahi-6204, Bangladesh
Md. Ashraful Huq

Department of Mathematics, Rajshahi University of Engineering and Technology, Kazla, Rajshahi-6204, Bangladesh
M. Kamrul Hasan

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - A New Straightforward Method for Evaluating Singular Integrals
AU  - Md. Habibur Rahaman
AU  - Md. Ashraful Huq
AU  - M. Kamrul Hasan
Y1  - 2015/10/13
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150406.14
DO  - 10.11648/j.acm.20150406.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 420
EP  - 423
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150406.14
AB  - 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.
VL  - 4
IS  - 6
ER  -

Copy | Download