High-order quadratures for integral operators with singular kernels
High-order quadratures for integral operators with singular kernels
复制标题
具有奇异核的积分算子的高阶求积
DOI：
10.1016/0377-0427(94)00040-8
复制
发表时间：
1995
影响因子：
2.4
通讯作者：
B. Alpert
中科院分区：
文献类型：
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作者：
B. Alpert
提出了一种对已知奇点的被积函数具有快速收敛性的数值积分方法。基于梯形法则的端点修正，该求积法适用于数学物理中遇到的各种积分方程的离散化。求积是基于Rokhlin（1990）引入的技术。本修改控制的增长的正交权重，并允许在实践中的高阶规则。几个数值例子。
A numerical integration method that has rapid convergence for integrands with known singularities is presented. Based on endpoint corrections to the trapezoidal rule, the quadratures are suited for the discretization of a variety of integral equations encountered in mathematical physics. The quadratures are based on a technique introduced by Rokhlin (1990). The present modification controls the growth of the quadrature weights and permits higher-order rules in practice. Several numerical examples are included.