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/...

Abstract We study the surface of Gauss double points associated to a very general quartic and natural morphisms it.

Abstract In this paper, we consider the Gauss-Kronrod quadrature formulas for a modified Chebyshev weight. Efficient estimates of error these Gauss–Kronrod formulae analytic functions are obtained, using techniques contour integration that were introduced by Gautschi and Varga (cf. SIAM J. Numer. Anal. 20 , 1170–1186 1983). Some illustrative numerical examples which show both accuracy sharpness...

In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...

In this paper, we consider a class of fractional-order differential equations and investigate two aspects these equations. First, the existence unique solution, then, using new control functions, Gauss hypergeometric stability. We use Chebyshev Bielecki norms in order to prove by Picard method. Finally, give some examples illustrate our results.

In this paper, we introduce the class of $(\beta,\gamma)$-Chebyshev functions and corresponding points, which can be seen as a family {\it generalized} Chebyshev polynomials points. For functions, prove that they are orthogonal in certain subintervals $[-1,1]$ with respect to weighted arc-cosine measure. particular investigate cases where become polynomials, deriving new results concerning clas...

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.