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Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions

Published online by Cambridge University Press:  28 May 2015

Ran Yu ,
Zhaoliang Meng  and
Zhongxuan Luo
Ran Yu*
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P.R. China
Zhaoliang Meng*
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P.R. China
Zhongxuan Luo*
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P.R. China School of Software, Dalian University of Technology, Dalian, 116620, P.R. China
*
Corresponding author.Email address:ranyu0602@sina.com
Corresponding author.Email address:mzhl@dlut.edu.cn
Corresponding author.Email address:zxluo@dlut.edu.cn
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Abstract

A simple method is proposed for constructing fourth-degree cubature formulae over general product regions with no symmetric assumptions. The cubature formulae that are constructed contain at most n2 + 7n + 3 nodes and they are likely the first kind of fourth-degree cubature formulae with roughly n2 nodes for non-symmetric integrations. Moreover, two special cases are given to reduce the number of nodes further. A theoretical upper bound for minimal number of cubature nodes is also obtained.

Keywords

65D3065D32Fourth-degree cubature formulacubature formulaproduct regionnon-symmetric regionnumerical integration
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 2 , May 2014 , pp. 179 - 192
Copyright
Copyright © Global Science Press Limited 2014

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