On The Boundary Type Cubature In Multiple Numerical Integration

The construction of boundary type cubature is a problem that has been noticed for a very long time in numerical integration. In some fields of applied mathematics and practical applications, such question can be encountered: how to calculate the domain integral when we only know some function values on the boundary? The boundary type cubature is quite the type of formulae that only use numerical values on the boundary of the domain. It undoubtedly has theoretical and instrumental value.This paper makes some research on the boundary type cubature in multiple integrals using Xu Lizhi method of reduction of dimensions. After constructing the boundary type cubature on the n-dimensional sphere and n-dimensional simplex, we make some comparisons on the results and some conclusions about the key problems in the process of formulae construction are given. At the same time, some questions need to be solved are raised.