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

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

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.