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On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations

Received: 31 May 2017     Accepted: 13 June 2017     Published: 17 July 2017
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Abstract

The Haar wavelet method applied to different kinds of integral equations (Fredholm integral equation, integro-differential equations and system of linear Fredholm integral equations) and boundary value problems (BVP) representation of integral equations. Three test problems whose exact solutions are known were considered to measure the performance of Haar wavelet. The calculations show that solving the problem as integral equation is more accurate than solving it as differential equation. Also the calculations show the efficiency of Haar wavelet in case of F. I. E. S and integro-differential equations comparing with other methods, especially when we increase the number of collocation points. All calculations are done by the Computer Algebra Facilities included in Mathematica 10.2.

Published in Mathematics and Computer Science (Volume 2, Issue 4)
DOI 10.11648/j.mcs.20170204.12
Page(s) 39-46
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), 2017. Published by Science Publishing Group

Keywords

Integral Equations, Haar Wavelets, BVP, System of Integral Equations, Collocation Method

References
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[3] Youssef, I. K., Ibrahim, R. A. “Boundary value problems, Fredholm integral equations, SOR and KSOR methods”, Life Science Journal, 10 (2), (2013) 304-312.
[4] H. A. El-Arabawy, I. K. Youssef, A symbolic algorithm for solving linear two-point Boundary value problems by modified Picard technique, Mathematical and Computer Modeling, 49 (2009) 344-351.
[5] E. Babolian, J. Biazar & A. R. Vahidi, The decomposition method applied to systems of Fredholm integral equations of the second kind, Applied Mathematics and Computation, 148 (2004) 443–452.
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[11] U. Lepik, Application of Haar wavelet transform to solving integral and differential equations, Applied Mathematics and Computation, 57 (1) (2007) pp. 28-46.
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Cite This Article
  • APA Style

    I. K. Youssef, R. A. Ibrahim. (2017). On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations. Mathematics and Computer Science, 2(4), 39-46. https://doi.org/10.11648/j.mcs.20170204.12

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    ACS Style

    I. K. Youssef; R. A. Ibrahim. On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations. Math. Comput. Sci. 2017, 2(4), 39-46. doi: 10.11648/j.mcs.20170204.12

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    AMA Style

    I. K. Youssef, R. A. Ibrahim. On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations. Math Comput Sci. 2017;2(4):39-46. doi: 10.11648/j.mcs.20170204.12

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  • @article{10.11648/j.mcs.20170204.12,
      author = {I. K. Youssef and R. A. Ibrahim},
      title = {On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations},
      journal = {Mathematics and Computer Science},
      volume = {2},
      number = {4},
      pages = {39-46},
      doi = {10.11648/j.mcs.20170204.12},
      url = {https://doi.org/10.11648/j.mcs.20170204.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170204.12},
      abstract = {The Haar wavelet method applied to different kinds of integral equations (Fredholm integral equation, integro-differential equations and system of linear Fredholm integral equations) and boundary value problems (BVP) representation of integral equations. Three test problems whose exact solutions are known were considered to measure the performance of Haar wavelet. The calculations show that solving the problem as integral equation is more accurate than solving it as differential equation. Also the calculations show the efficiency of Haar wavelet in case of F. I. E. S and integro-differential equations comparing with other methods, especially when we increase the number of collocation points. All calculations are done by the Computer Algebra Facilities included in Mathematica 10.2.},
     year = {2017}
    }
    

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    AB  - The Haar wavelet method applied to different kinds of integral equations (Fredholm integral equation, integro-differential equations and system of linear Fredholm integral equations) and boundary value problems (BVP) representation of integral equations. Three test problems whose exact solutions are known were considered to measure the performance of Haar wavelet. The calculations show that solving the problem as integral equation is more accurate than solving it as differential equation. Also the calculations show the efficiency of Haar wavelet in case of F. I. E. S and integro-differential equations comparing with other methods, especially when we increase the number of collocation points. All calculations are done by the Computer Algebra Facilities included in Mathematica 10.2.
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Author Information
  • Department of Mathematics, Ain Shams University, Cairo, Egypt

  • Department of Mathematics and Engineering Physics, Faculty of Engineering_Shoubra, Benha University, Cairo, Egypt

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