An Iterative Method for Solving Two Dimensional Nonlinear Volterra Integral Equations

Document Type : Research Paper


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 integral
equations is proposed. This algorithm uses a trapezoidal quadrature rule for Lipschitzian functions
applied 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.