ON IGNORING THE SINGULARITY IN NUMERICAL QUADRATURE.

Abstract

Recent papers of P. Davis and P. Rabinowitz and of P. Rabinowitz study the problem of 'ignoring the singularity' in numerical quadrature of singular integrands. Among the other things they show that for certain quadratures if the singularity occurs at an end point of the interval and if the integrand is monotone in a neighborhood of this singularity, then the quadrature does indeed approximate the integral. The purpose of this paper is to show that the assumption of monotonicity of the integrand can be replaced by the assumption that the integrand can be dominated by a monotone, integrable function. The paper also contains error estimates for approximate quadratures of singular integrands. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1969
Accession Number
AD0696145

Entities

People

  • R. K. Miller

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Integrals
  • Intervals
  • Mathematics
  • Numerical Quadrature

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Military History of the United States in the 20th Century.