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Indexed by:期刊论文

Date of Publication:2011-11-01

Journal:APPLIED MATHEMATICS AND COMPUTATION

Included Journals:Scopus、SCIE、EI

Volume:218

Issue:5

Page Number:2036-2043

ISSN No.:0096-3003

Key Words:Numerical integration formulas of degree three; Cubature formulas; Orthogonal polynomial; Numerical integrations

Abstract:Numerical integration formulas in n-dimensional Euclidean space of degree three are discussed. In this paper, for the product regions a method is presented to construct numerical integration formulas of degree three with 2n real points and positive weights. The presented problem is a little different from those dealt with by other authors. All the corresponding one-dimensional integrals can be different from each other and they are also nonsymmetrical. In this paper an n-dimensional numerical integration problem is turned into n one-dimensional moment problems, which simplifies the construction process. Some explicit numerical formulas are given. Furthermore, a more generalized numerical integration problem is considered, which will shed light on the final solution to the third degree numerical integration problem. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.