In this paper, a numerical scheme is utilized to solve three‐dimensional nonlinear system of Volterra‐Hammerstein integrals equations, which is based on the three‐dimensional block‐pulse functions (3D‐BPFs) and their operational matrices. Then the primary nonlinear system is transferred into a linear system of algebraic equations by applying the approximate expression and operational matrices, which can be easily solved through any numerical techniques. According to the convergence of 3D‐BPFs, the new convergence analysis and error estimation theorem of the research system is detailed investigated. Lastly illustrative examples are included to demonstrate the validity and applicability of the technique.

中文翻译：

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应用三维块脉冲函数求解Volterra-Hammerstein积分方程组

在本文中，基于三维分块脉冲函数（3D-BPF）及其运算矩阵，采用数值方案求解Volterra-Hammerstein积分方程的三维非线性系统。然后，通过应用近似表达式和运算矩阵，将初级非线性系统转换为代数方程式的线性系统，可以通过任何数值技术轻松地将其求解。根据3D-BPF的收敛性，详细研究了研究系统的新的收敛性分析和误差估计定理。最后包括说明性示例以证明该技术的有效性和适用性。