In this work, we describe a numerical scheme based on modified moving least-square (MMLS) method for solving Fredholm–Hammerstein integral equations on 2D irregular domains. The moment matrix in moving least squares (MLS) method may be singular when the number of points in the local support domain is not enough. To overcome this problem, the MMLS method with non-singular moment matrix is used. The basic advantage of the proposed method does not require any adaptation of the nodal density in non-rectangular domain and the results converge more quickly to the exact solution. The error bound for the proposed method is provided. The new technique is examined in various integral equations and compared with the classical MLS method to show the accuracy and computational efficiency of the method.

在这项工作中，我们描述了一种基于修正移动最小二乘法 (MMLS) 的数值方案，用于求解二维不规则域上的 Fredholm-Hammerstein 积分方程。当局部支持域中的点数不够时，移动最小二乘法 (MLS) 中的矩矩阵可能是奇异的。为了克服这个问题，使用了具有非奇异矩矩阵的 MMLS 方法。所提出方法的基本优点是不需要对非矩形域中的节点密度进行任何调整，并且结果可以更快地收敛到精确解。提供了所提出方法的误差界限。新技术在各种积分方程中进行了检查，并与经典的 MLS 方法进行了比较，以显示该方法的准确性和计算效率。