Before revision:  This paper also introduces several methods for smoothing integrands with point singularities and near-singularities based on the generalized Duffy transformation 3 and a distance transformation described in Ma and Kamiya 4 . When these methods are combined , highly efficient integration of weakly-singular functions is realized.
After revision:  This paper also introduces several methods for smoothing integrands with point singularities and near-singularities based on the generalized Duffy transformation 3 4 . When these methods are combined , highly efficient integration of weakly-singular functions is realized.