Abstract In this article, different types of Gaussian quadrature methods have been presented to find the numerical integration a neutrosophic valued function. A new definition distance between two number has defined and it proved that set all form complete metric space. Also, continuity on closed-bounded interval in sense $$(\alpha ,\beta ,\gamma )$$ <mml:math xmlns:mml="http://www.w3.org/1998/...

Procedures are described for the high-precision calculation of the modiied Bessel function K(x), 0 < < 1, and the Airy function Ai(x), for positive arguments x, as prerequisites for generating Gaussian quadrature rules having these functions as weight function.

them particularly important in solvinG physical problems. Also, Gaussian integration provides a highly accurate and efficient algorithm for integrating functions. The value of the methods I describe in this installment of “Computing Prescriptions” depends on the basic assumption that a finite-order polynomial can effectively approximate a function. Therefore, a finite sum of orthogonal polynomi...

We propose a novel form of sequential Monte Carlo integration that emerges from a decisiontheoretic treatment of approximation. Quadrature of any kind requires a set of samples of the integrand. Bayesian quadrature [O’Hagan, 1991, Rasmussen and Ghahramani, 2003] employs those samples within a Gaussian process framework to perform inference about unobserved regions of the space, and hence about ...