Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 7 2 2022 09 01 Numerical Integration of Symmetric Multivariate Function 151 159 300 10.22128/gadm.2022.480.1058 EN Mohammad Gholami Baladezaei Department of Applied Mathematics, Faculty of Sciences, Islamic Azad University, Damghan Branch, Damghan, Iran 0000-0001-9290-7766 Morteza Gachpazan Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran Journal Article 2021 11 22 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. https://ansne.du.ac.ir/article_300_354844167cb3ed966fae0795ef6aa55b.pdf