Volume 2, Issue 4, July 2017, Page: 39-46
On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations
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
Received: May 31, 2017;       Accepted: Jun. 13, 2017;       Published: Jul. 17, 2017
DOI: 10.11648/j.mcs.20170204.12      View  1855      Downloads  79
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.
Keywords
Integral Equations, Haar Wavelets, BVP, System of Integral Equations, Collocation Method
To cite this article
I. K. Youssef, R. A. Ibrahim, On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations, Mathematics and Computer Science. Vol. 2, No. 4, 2017, pp. 39-46. doi: 10.11648/j.mcs.20170204.12
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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