We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for the hypercube: this is the merit of a rule which is closely related to its trigonometric degree and which reduces to the Zaremba figure of merit in the case of a lattice rule. We derive a family of rules Q k having dimension s and merit 2. These rules seem to be competitive with lattice rules with...

This article is concerned with a new method for the approximate evaluation of Fourier sine and cosine transforms. We develope and analyse a new quadrature rule for Fourier sine and cosine transforms involving transforming the integral to one over the entire real line and then using the trapezoidal rule in order to approximate the transformed integral. This method follows on from the work of Oou...

Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0, ) ∞ and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluat...

A high-accuracy prescription (quadrature rule) is the set of points Xj and weights Wj such that the error E (n) is a small and rapidly decreasing function of n, the number of mesh points used. Now suppose we want to integrate a function F(X l ,x2'''''Xd) = F(x) over the d-dimensional cube. The direct product technique would be to use the rule (1) d timesi ". n2 "d L L '" L Wj, Wh ... wjdF (Xj" ...

This paper establishes properties of discrete orthogonal projections on periodic spline spaces of order r, with knots that are equally spaced and of arbitrary multiplicity M ≤ r. The discrete orthogonal projection is expressed in terms of a quadrature rule formed by mapping a fixed J -point rule to each sub-interval. The results include stability with respect to discrete and continuous norms, c...

A new angular quadrature type termed Modified Simpson Trapezoidal (MST) is developed based on the conventional Simpson’s 1/3 rule where pattern over polar levels has a trapezoid shape. An adaptive coefficient correction scheme to enable our integrate flux subintervals separated by interior jump irregularities. two-dimensional test problem employed verify discretization error in uncollided S N s...

In this paper, we introduce a new three-step Newton method for solving system of nonlinear equations. This based on Gauss quadrature rule has sixth order convergence (with n=3). The proposed solves boundary-value problems and integral equations in few iterations with good accuracy. Numerical comparison shows that the is remarkably effective systems