Convergence of 2D-orthonormal Bernstein collocation method for solving 2D-mixed Volterra–Fredholm integral equations

Abstract In this paper, an efficient numerical method is used for solving 2D-mixed Volterra–Fredholm integral equations. This method is based on 2D-orthonormal Bernstein polynomials (2D-OBPs) together with collocation method. This approach is applied to convert the problem under study into a system of algebraic equations which can be solved by using a convenient numerical method. Several useful theorems are proved which are concerned with the convergence and error estimate associated to the suggested scheme. Finally, by comparing the values of absolute error achieved from this method with values of absolute error obtained from other previous methods, we show that this method is very accurate and efficient.