A collocation method based on Bernstein polynomials to solve nonlinear Fredholm–Volterra integro-differential equations

In this study, a collocation method that based on Bernstein polynomials is presented for nonlinear Fredholm–Volterra integro-differential equations (NFVIDEs). By means of the collocation method and the matrix operations, the problem is reduced into a system of the nonlinear algebraic equations. The approximate solutions are obtained by solving this nonlinear system. Error analysis is presented for the Bernstein series solutions of the nonlinear Fredholm–Volterra integro-differential equations. Several examples are given to illustrate the efficiency and implementation of the proposed method for solving the NFVIDEs. Comparisons are made to confirm the reliability of the method. Also error analysis is applied for the numerical examples.