TY - EJOU
AU - Li, Jin
AU - Ru, Hongxing
AU - Yu, Dehao
TI - Composite Simpsonâ€™s Rule for Computing Supersingular Integral on Circle
T2 - Computer Modeling in Engineering \& Sciences
PY - 2014
VL - 97
IS - 6
SN - 1526-1506
AB - The computation with Simpsonâ€™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.
KW - Supersingular integral
KW - Composite Simpson rule
KW - Error Expansion
KW - Superconvergence
DO - 10.3970/cmes.2014.097.463