Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations based on the Bernstein polynomials method

This work approximates the unknown functions based on the Bernstein polynomials, in conjunction with the collocation method for the numerical solution of nonlinear Fredholm-Volterra-Hammerstein integral equations. In this method, the problem will be converted to system of two equations and then this system will be reduced to a system of nonlinear algebraic equations that can be easily solved by any usual numerical methods. The convergence analysis of proposed method has been discussed through some theorems. Finally, a numerical example is given to show the superiority and efficiency of proposed method in comparison with some other well-known methods.