Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 179-192.
Published online: 2014-07
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.y12038}, url = {http://global-sci.org/intro/article_detail/nmtma/5870.html} }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.