论文标题
非线性弱奇异积分方程的两种数值方法
Two Numerical Approaches for Nonlinear Weakly Singular Integral Equations
论文作者
论文摘要
线性弱奇异的弗雷德·弗雷姆（Fredholm）积分方程的奇异性减法被推广到非线性积分方程。提出了两种方法：经典方法离散了非线性问题，并使用一些有限的维度线性化过程来求解离散问题。在对非线性和奇异性减法方案的非线性规则的轻度假设下，其收敛性得到了证明。新方法是基于问题在其无限维度设置中的线性化，以及通过奇异性减法对线性问题序列的离散化。正如两个数值实验所证实的那样，它比前者更有效。
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.
