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    Composite Simpson’s Rule for Computing Supersingular Integral on Circle

    Jin Li1,2, Hongxing Ru1, Dehao Yu3,4

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.6, pp. 463-482, 2014, DOI: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. More >

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