Advances in Difference Equations
, 2013:123
First online:
Numerical solution of linear integral equations system using the Bernstein collocation method
 Ahmad JafarianAffiliated withDepartment of Mathematics, Islamic Azad University
 , Safa A Measoomy NiaAffiliated withDepartment of Mathematics, Islamic Azad University
 , Alireza K GolmankhanehAffiliated withDepartment of Physics, Islamic Azad University
 , Dumitru BaleanuAffiliated withDepartment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Çankaya UniversityDepartment of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz UniversityInstitute of Space Sciences Email author
Abstract
Since in some application mathematical problems finding the analytical solution is too complicated, in recent years a lot of attention has been devoted by researchers to find the numerical solution of this equations. In this paper, an application of the Bernstein polynomials expansion method is applied to solve linear second kind Fredholm and Volterra integral equations systems. This work reduces the integral equations system to a linear system in generalized case such that the solution of the resulting system yields the unknown Bernstein coefficients of the solutions. Illustrative examples are provided to demonstrate the preciseness and effectiveness of the proposed technique. The results are compared with the exact solution by using computer simulations.
 Title
 Numerical solution of linear integral equations system using the Bernstein collocation method
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Advances in Difference Equations
2013:123
 Online Date
 May 2013
 DOI
 10.1186/168718472013123
 Online ISSN
 16871847
 Publisher
 Springer International Publishing
 Additional Links
 Topics
 Authors

 Ahmad Jafarian ^{(1)}
 Safa A Measoomy Nia ^{(1)}
 Alireza K Golmankhaneh ^{(2)}
 Dumitru Baleanu ^{(3)} ^{(4)} ^{(5)}
 Author Affiliations

 1. Department of Mathematics, Islamic Azad University, Urmia Branch, Urmia, Iran
 2. Department of Physics, Islamic Azad University, Urmia Branch, Urmia, Iran
 3. Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Çankaya University, Balgat, Ankara, 0630, Turkey
 4. Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia
 5. Institute of Space Sciences, P.O. Box MG23, Magurele, Bucharest, 76900, Romania