ENGLISH

Hybrid Gauss-trapezoidal quadrature

By Alpert.

Book information

Language
english
Format
DJVU
Filesize
210 kB (215389 bytes)
Pages
34\34
Library
kolxoz
Time added
2009-07-20 03:45:11

Description

A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily high-order convergence. The quadratures result from alterations to the trapezoidal rule, in which a small number of nodes and weights at the ends of the integration interval are replaced. The new nodes and weights are determined so that the asymptotic expansion of the resulting rule, provided by a generalization of the Euler - Maclaurin summation formula, has a prescribed number of vanishing terms. The superior performance of the rules is demonstrated with numerical examples and application to several problems is discussed.

Similar books