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

I. K. Youssef; R. A. Ibrahim

doi:doi:10.11648/j.mcs.20170204.12

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

I. K. Youssef, R. A. Ibrahim

Published in Mathematics and Computer Science (Volume 2, Issue 4)

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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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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TY  - JOUR
T1  - On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations
AU  - I. K. Youssef
AU  - R. A. Ibrahim
Y1  - 2017/07/17
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JO  - Mathematics and Computer Science
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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

I. K. Youssef

Department of Mathematics, Ain Shams University, Cairo, Egypt
R. A. Ibrahim

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

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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}
}

Copy | Download

TY  - JOUR
T1  - On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations
AU  - I. K. Youssef
AU  - R. A. Ibrahim
Y1  - 2017/07/17
PY  - 2017
N1  - https://doi.org/10.11648/j.mcs.20170204.12
DO  - 10.11648/j.mcs.20170204.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 39
EP  - 46
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20170204.12
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.
VL  - 2
IS  - 4
ER  -

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