Extended Gaussian quadratures for functions with an end-point singularity of logarithmic type

Published: 1 January 2014| Version 1 | DOI: 10.17632/5m9n4vyxg9.1
K. Pachucki, M. Puchalski, V.A. Yerokhin


Abstract The extended Gaussian quadrature rules are shown to be an efficient tool for numerical integration of wide class of functions with singularities of logarithmic type. The quadratures are exact for the functions pol1 _(n-1)(x)+lnxpol2_(n-1)(x), where pol1_(n-1)(x) and pol2_(n-1)(x) are two arbitrary polynomials of degree n-1 and n is the order of the quadrature formula. We present an implementation of numerical algorithm that calculates the nodes and the weights of the quadrature formul... Title of program: GAUSEXT Catalogue Id: AETP_v1_0 Nature of problem Quadrature formulas for numerical integration, effective for a wide class of functions with end-point singularities of logarithmic type. Versions of this program held in the CPC repository in Mendeley Data AETP_v1_0; GAUSEXT; 10.1016/j.cpc.2014.06.018 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)



Computational Physics, Computational Method