The purpose of this study is to construct a new efficient iterative method of successive approximation based on the three-point Simpson quadrature rule for solving three-dimensional nonlinear Fredholm integral equations. We have also provided the convergence and error analysis of the proposed method. Furthermore, we present the numerical stability analysis of the method with respect to the choice of the first iteration. Finally, some numerical experiments illustrate the accuracy of the method.

中文翻译：

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逼近三维非线性Fredholm积分方程的解

这项研究的目的是构造一个新的有效的逐次逼近迭代方法，该方法基于三点Simpson正交法则来求解三维非线性Fredholm积分方程。我们还提供了该方法的收敛性和误差分析。此外，我们提出了关于第一次迭代选择的方法的数值稳定性分析。最后，一些数值实验证明了该方法的准确性。