Accession Number : AD0696145

Title :   ON IGNORING THE SINGULARITY IN NUMERICAL QUADRATURE.

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Miller,R. K.

Report Date : OCT 1969

Pagination or Media Count : 21

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)

Descriptors :   (*NUMERICAL INTEGRATION, NUMERICAL ANALYSIS), APPROXIMATION(MATHEMATICS), INTEGRALS, INEQUALITIES, CONVERGENCE, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE