A particular case of the Hermite interpolation method, namely the two-point Taylor formula, is utilized to construct a numerical technique for solving Fredholm integral equations (FIEs) of the second kind. This method can be applied to approximate the solution of both linear and nonlinear FIEs, and systems of nonlinear FIEs. The sufficient conditions to guarantee the convergence of the proposed method are provided through our analytical studies. Also, the error estimation is presented for this method. Furthermore, the efficiency of the method is confirmed by applying it to solve several illustrative examples. Numerical experiments confirm that the method is easy to implement and gives accurate approximations in acceptable computational times.

利用Hermite插值方法的一种特殊情况，即两点泰勒公式，来构造一种数值技术，用于求解第二种Fredholm积分方程（FIE）。该方法可用于近似线性和非线性FIE以及非线性FIE系统的解。通过我们的分析研究，提供了保证所提出方法收敛的充分条件。另外，针对该方法提出了误差估计。此外，通过将其应用于解决几个说明性示例来确认该方法的效率。数值实验证实了该方法易于实现，并在可接受的计算时间内给出了精确的近似值。