Open Access

ARTICLE

Composite Simpson’s Rule for Computing Supersingular Integral on Circle

Jin Li^1,2, Hongxing Ru¹, Dehao Yu^3,4

1 School of Mathematics, Shandong University, Jinan, 250100, PR China
2 School of Sciences, Shandong Jianzhu University, Jinan 250101, China.
3 School of Mathematical Sciences, Xiamen University, Xiamen 361005, China.
4 LSEC, ICMSEC, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190, China.

Computer Modeling in Engineering & Sciences 2014, 97(6), 463-482. https://doi.org/10.3970/cmes.2014.097.463

Abstract

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.

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Keywords

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