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.
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Kazemi, M. (2021). An Iterative Method for Solving Two Dimensional Nonlinear Volterra Integral Equations. Global Analysis and Discrete Mathematics, 6(1), 41-57. doi: 10.22128/gadm.2021.383.1036
MLA
Manochehr Kazemi. "An Iterative Method for Solving Two Dimensional Nonlinear Volterra Integral Equations". Global Analysis and Discrete Mathematics, 6, 1, 2021, 41-57. doi: 10.22128/gadm.2021.383.1036
HARVARD
Kazemi, M. (2021). 'An Iterative Method for Solving Two Dimensional Nonlinear Volterra Integral Equations', Global Analysis and Discrete Mathematics, 6(1), pp. 41-57. doi: 10.22128/gadm.2021.383.1036
VANCOUVER
Kazemi, M. An Iterative Method for Solving Two Dimensional Nonlinear Volterra Integral Equations. Global Analysis and Discrete Mathematics, 2021; 6(1): 41-57. doi: 10.22128/gadm.2021.383.1036