Singularity subtraction for linear weakly singular Fredholm integral equations of the second kind is generalized to nonlinear integral equations. Two approaches are presented: The Classical Approach discretizes the nonlinear problem, and uses some finite dimensional linearization process to solve numerically the discrete problem. Its convergence is proved under mild hypotheses on the nonlinearity and the quadrature rule of the singularity subtraction scheme. The New Approach is based on linearization of the problem in its infinite dimensional setting, and discretization of the sequence of linear problems by singularity subtraction. It is more efficient than the former, as two numerical experiments confirm.

翻译：对线性微弱单一的Fredholm 二类整体方程式的单项减法,一般为非线性整体方程式。提出了两种方法:古典方法将非线性问题分解,并使用某些有限维线性线性进程从数字上解决离散问题。在非线性和非单项减法方案的二次规则的轻度假设下证明了其趋同性。新方法基于其无限维度设置中问题的线性化,以及单数减法将线性问题序列分解。它比前一种方法更有效,因为两个数字实验证实了这一点。