Manochehr Kazemi - Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran

In this paper, a numerical iterative algorithm based on combination of the successive approximations method and the quadrature formula for solving two-dimensional nonlinear Volterra integralequations is proposed. This algorithm uses a trapezoidal quadrature rule for Lipschitzian functionsapplied at each iterative step. The convergence analysis and error estimate of the method are proved.Finally, two numerical examples are presented to show the accuracy of the proposed method.

Two-dimensional nonlinear integral equations, Trapezoidal cubature formula, Iterative method, Successive approximations