Computational method based on Bernstein operational matrices for nonlinear Volterra–Fredholm–Hammerstein integral equations

In this paper, we present a method to solve nonlinear Volterra–Fredholm–Hammerstein integral equations in terms of Bernstein polynomials. Properties of these polynomials and operational matrix of integration together with the product operational matrix are first presented. These properties are then utilized to transform the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Bernstein coefficients. The method is computationally very simple and attractive and numerical examples illustrate the efficiency and accuracy of the method.