Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 2 : pp. 179–192
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 $n^2+7n+3$ nodes and they are likely the first kind of fourth-degree cubature formulae with roughly $n^2$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2014.y12038
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 2 : pp. 179–192
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Fourth-degree cubature formula cubature formula product region non-symmetric region numerical integration.