Bernstein polynomials method for solving Volterra-Fredholm integral equations

In this paper, a new algorithm for solving the Volterra-Fredholm integral equations is presented. This method approximates the unknown function with Bernstein polynomials. The merits of this method lie in the fact that, on the one hand, the problem will be reduced to a system of algebraic equations. On the other hand, the efficiency and accuracy of the Bernstein polynomials method (BPM) for solving these equations are high, which will be shown by preparing some theorems. This method is using a simple computational manner to obtain a quite acceptable approximate solution. Finally, some examples are given to confirm the superiority and efficiency of present method with respect to some other well-known methods such as the Legendre collocation method (LECM), Taylor collocation method (TCM), Taylor polynomial method (TPM) and Lagrange collocation method (LACM).