论文标题
一类高阶校正的梯形规则的收敛
Convergence of a class of high order corrected trapezoidal rules
论文作者
论文摘要
我们介绍了校正的正交规则的融合理论，该规则均匀的笛卡尔网格具有点奇异性的功能。首先，我们得出对穿刺的梯形规则的错误估计，然后得出误差扩展。我们基于刺穿的梯形规则来定义校正后的梯形规则，在这些规则中，根据这些扩展，明智地纠正了接近奇异性的节点的权重。然后，我们使用围绕点奇异性并适当应用校正后的梯形规则来定义更大的功能系列的复合校正的梯形规则。我们证明，我们可以通过使用足够数量的点奇异性和扩展项来实现高阶精度。
We present convergence theory for corrected quadrature rules on uniform Cartesian grids for functions with a point singularity. We begin by deriving an error estimate for the punctured trapezoidal rule, and then derive error expansions. We define the corrected trapezoidal rules, based on the punctured trapezoidal rule, where the weights for the nodes close to the singularity are judiciously corrected based on these expansions. Then we define the composite corrected trapezoidal rules for a larger family of functions using series expansions around the point singularity and applying corrected trapezoidal rules appropriately. We prove that we can achieve high order accuracy by using a sufficient number of correction nodes around the point singularity and of expansion terms.
