Numerical solution of two-dimensional nonlinear Volterra integral equations using Bernstein polynomials

Abstract

The purpose of this paper is to present a numerical method for finding an approximate solution of two-dimensional (2D) nonlinear volterra integral equations. First, we introduce two-dimensional Bernstein functions, then present their operational matrices of integration and product. Using this properties and collcation points, reduce integral equation to a system of nonlinear algebric equations. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique.