Symmetric quadrature rules on a triangle

A Set of Symmetric Quadrature Rules on Triangles and Tetrahedra

We present a program for computing symmetric quadrature rules on triangles and tetrahedra. A set of rules are obtained by using this program. Quadrature rules up to order 21 on triangles and up to order 14 on tetrahedra have been obtained which are useful for use in finite element computations. All rules presented here have positive weights with points lying within the integration domain. Mathe...

New fully symmetric and rotationally symmetric cubature rules on the triangle using minimal orthonormal bases

Cubature rules on the triangle have been extensively studied, as they are of great practical interest in numerical analysis. In most cases, the process by which new rules are obtained does not preclude the existence of similar rules with better characteristics. There is therefore clear interest in searching for better cubature rules. Here we present a number of new cubature rules on the triangl...

Quadrature Rules for Fuzzy Integrals

A constraint on extensible quadrature rules

When the worst case integration error in a family of functions decays as n−α for some α > 1 and simple averages along an extensible sequence match that rate at a set of sample sizes n1 < n2 < · · · < ∞, then these sample sizes must grow at least geometrically. More precisely, nk+1/nk ≥ ρmust hold for a value 1 < ρ < 2 that increases with α. This result always rules out arithmetic sequences but ...

Quadrature rules on unbounded interval

After some remarks on the convergence order of the classical gaussian formula for the numerical evaluation of integrals on unbounded interval, the authors develop a new quadrature rule for the approximation of such integrals of interest in the practical applications. The convergence of the proposed algorithm is considered and some numerical examples are given.