Numerical Integration of Symmetric Multivariate Function

In this paper, we introduce a method for finding the integral of symmetric multivariate function. We compute the number of nodes which the method use them, and also by using the Gauss-Legendre integrating, we obtain the approximate value the generalized symmetric function. Theoretical consideration has been discussed and some examples were presented to show the ability of the method for approximate value of integral of the symmetric functions. In this numerical integration approach, for a symmetric function that has the same calculations at a number of different node points, only calculations are performed for a node and the result is multiplied by the number of repetitions of similar cases. In addition to modulating errors due to rounding and expanded error during calculations, much less memory is used than the numerical integration method. Also in this approach, the time of numerical integration is reduced and the numerical results confirm this.