In this paper, a new numerical iterative method based on the successive approximations method for solving nonlinear Hammerstein Volterra integral equations of the second kind is proposed. The main approximation tool is based on triangular functions. Also, the convergence analysis and numerical stability of the proposed method are proved. Finally, some numerical examples verify the theoretical results and show the accuracy of the method.

中文翻译：

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非线性 Volterra 积分方程数值解的三角函数

本文提出了一种基于逐次逼近法求解非线性Hammerstein Volterra积分方程的新的数值迭代方法。主要的近似工具基于三角函数。同时，证明了所提方法的收敛性分析和数值稳定性。最后,通过数值算例验证了理论结果,证明了该方法的准确性。