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

Advances in Difference Equations

Dumitru Baleanu¹  Safa A Measoomy Nia²  Ahmad Jafarian²  Alireza K Golmankhaneh³ 

[1] Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, ÇDepartment of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran;Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran;ankaya University, Balgat, Turkey

关键词: Integral Equation;    Homotopy Analysis Method;    Fredholm Integral Equation;    Volterra Integral Equation;    Bernstein Polynomial;   

DOI  :  10.1186/1687-1847-2013-123

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY