Research Article

Advances in Difference Equations

, 2013:123

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Numerical solution of linear integral equations system using the Bernstein collocation method

  • Ahmad JafarianAffiliated withDepartment of Mathematics, Urmia Branch, Islamic Azad University
  • , Safa A Measoomy NiaAffiliated withDepartment of Mathematics, Urmia Branch, Islamic Azad University
  • , Alireza K GolmankhanehAffiliated withDepartment of Physics, Urmia Branch, 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 


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.