标题：Composite Simpson\'s Rule for Computing Supersingular Integral on Circle
作者：Jin Li;Hongxing Ru;Dehao Yu
作者机构：[Li, J] School of Mathematics, Shandong University, Jinan,250100, China, School of Sciences, Shandong Jianzhu University, Jinan 250101, China;[ Ru, H] 更多
通讯作者地址：[Li, J]Shandong Univ, Sch Math, Jinan 250100, Peoples R China.
来源：Computer Modeling in Engineering & Sciences
关键词：Supersingular integral;Composite Simpson rule;Error Expansion;Superconvergence
摘要：The computation with Simpson\'s rule for the supersingular integrals on circle is discussed. When the singular point coincides with some priori known point, the convergence rate of the Simpson rule is higher than the globally one which is considered as the superconvergence phenomenon. Then the error functional of density function is derived and the superconvergence phenomenon of composite Simpson rule occurs at certain local coordinate of each subinterval. Based on the error functional, a modify quadrature is presented. At last, numerical examples are provided to validate the theoretical analysis and show the efficiency of the algorithms.