Numerical solution of Hammerstein integral equations by using combination of spline-collocation method and Lagrange interpolation

The numerical solutions to the nonlinear integral equations of the Hammerstein-type:y(t)=f(t)+∫01k(t,s)g(s,y(s))ds,t∈[0,1]with using B-splines functions are investigated. An interpolation method based on B-splines functions combined with a new collocation method is presented. Finally, for showing efficiency of the method we give some numerical examples.