F. Mirzaee - Department of Mathematics, Faculty of Science, Malayer University
S. Fathi - Department of Mathematics, Faculty of Science, Malayer University

In this study a numerical method is developed to solve the Hammerstein integral equations. To this end the kernel has been approximated using the leastsquares approximation schemes based on Legender-Bernstein basis. The Legender polynomials are orthogonal and these properties improve the accuracy of the approximations. Also the nonlinear unknown function has been approximated by using the Bernstein basis. The useful properties of Bernstein polynomials help us to transform Hammerstein integral equation to solve a system of nonlinear algebraic equations.    

Nonlinear Hammerstein integral equations, Bernstein basis, Legendre basis, Orthogonal polynomials