A collocation method for integral equations in terms of generalized Bernstein polynomials

Abstract

In this study, a collocation method based on generalized Bernstein polynomials is presented for approximate solution of Fredholm–Volterra integral equations.While this method is applicable directly to linear integral equations of the first, second and third kinds, it is applicable iteratively to nonlinear integral equations using method of quasilinearzation. Error bounds are demonstrated for the Bernstein collocation method, and the convergence of this method is shown, Moreover, some numerical examples are given to illustrate the accuracy, efficiency and applicability of the method.