Numerical integration of neutrosophic valued function by Gaussian quadrature methods

Abstract

In this article, different types of Gaussian quadrature methods have been presented to find the numerical integration of a neutrosophic valued function. A new definition of the distance between two neutrosophic number has been defined and it has been proved that the distance and the set of all neutrosophic number form a complete metric space. Also, the definition of neutrosophic continuity on a closed-bounded interval has been defined in the sense of $$(\alpha ,\beta ,\gamma )$$ ( α , β , γ ) -cut. This is the first time, when the Gauss–Legendre integration, Gauss–Chebyshev integration and Gauss–Laguerre integration rule have been discussed in neutrosophic environment. In the first test example, the comparison between one-point, two-point and three-point Gauss–Legendre integration rules have been presented in terms of tables and figures. Also, in the second example, the comparison between one-point, two-point Gauss–Chebyshev and Gauss–Laguerre integration rules have been discussed.