The cycle index polynomial of a symmetric group is a basic tool in combinatorics and especially in Pólya enumeration theory. It seems irrelevant to numerical analysis. Through Faá di Bruno’s formula, cycle index is connected with numerical analysis. In this work, the Hermite interpolation polynomial is explicitly expressed in terms of cycle index. Applications in Gauss-Turán quadrature formula ...

We give several descriptions of positive quadrature formulas which are exact for trigonometric-, respectively, Laurent polynomials of degree less or equal to n − 1 − m, 0 ≤ m ≤ n − 1. A complete and simple description is obtained with the help of orthogonal polynomials on the unit circle. In particular it is shown that the nodes polynomial can be generated by a simple recurrence relation. As a ...

in present study, thermo-elastic buckling analysis of multi-layer orthotropic annular/circular graphene sheets is investigated based on eringen’s theory. the moderately thick and also thick nano-plates are considered. using the non-local first and third order shear deformation theories, the governing equations are derived. the van der waals interaction between the layers is simulated for multi-...

in this paper, conjugate heat transfer of magneto hydrodynamic mixed convection of nanofluid about a vertical slender hollow cylinder embedded in a porous medium with high porosity have been numerically studied. the forchheimer’s modification of darcy’s law was used in representing the nanofluid motion inside the porous media. the governing boundary layer equations were transformed to non-dimen...

Each of these rules will be called a Gauss-Christoffel quadrature formula if it has maximum degree of exactness, i.e. if (1.1) is an exact equality whenever / is a polynomial of degree 2n — 1. It is a well-known fact, due to Christoffel [3], that such quadrature formulas exist uniquely, provided the weight function w(x) is nonnegative, integrable with /* w(x)dx > 0, and such that all its moments

In recent years a number of authors have considered an error analysis for quadrature rules of Newton-Cotes type. In particular, the mid-point, trapezoid and Simpson rules have been investigated more recently ([2], [4], [5], [6], [11]) with the view of obtaining bounds on the quadrature rule in terms of a variety of norms involving, at most, the first derivative. In the mentioned papers explicit...

A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the shells are treated separately with constructive filtered polynomial approximation. The approximation error with respect to the supremum norm is shown to decay alg...