Details of Research Outputs

The quadrature formulae of Newton-Cotes type for the computation of hypersingular integrals with second order singularity on interval are discussed. We improve the estimates given by Linz [22] such that the Newton-Cotes method is valid with less restriction on the location of the singular point. We also present a new Newton-Cotes formula which is applicable when the singular point coincides with a mesh point, while the classical Newton-Cotes method fails in this case. Error analysis for the new formula is given. Numerical experiments are presented to validate the analysis.