A wide range of numerical integration options are available in OpenSees to represent distributed plasticity or non-prismatic section details in force-based beam-column elements, i.e., across the entire element domain [0, L]. For the Tcl interpreter of OpenSees, there is a specific input format for each integration option that follows a common input format for the element tag, nodes, and transfo...

I discuss how to sample the space of parton momenta in order to best perform the numerical integrations that lead to a calculation of three jet cross sections and similar observables in electron-positron annihilation. Typeset using REVTEX

Upper and lower bounds for the discrepancy of nodes in lattice rules for multidimensional numerical integration are established. In this way the applicability of lattice rules is extended to nonperiodic integrands.

Computer Algebra Systems are developing very fast and it is now possible to use new computational power very efficiently to analytically integrate dynamical systems. However, the task of producing an appropriate program is time consuming and requires a considerable amount of skills and practice. Here the merits of numerical versus computer algebraic approaches are compared in the context of a s...

Chimera [10] happens to be a version of Schwarz' method and of Lions' space decomposition method (SDM). It was analyzed by Brezzi et al [1] but an estimate was missing for for numerical quadrature. We give it here with new numerical tests.

In the article, the noted Darboux’s formula of functions with single variable is generalized to that of functions of two independent variables with integral remainder, some important special cases of Darboux’s formula of functions with two variables are obtained, and some estimates of the integral remainders and Darboux’s expansion of the function ln(x + y) are given. These results generalize A...

ABSTRACT A scheme for systematically separating ultraviolet divergences of Feynrnan amplitudes in parametric space is developed. It is summarized by an explicit formula which enables us to incorporate readily the ultraviolet-finite remainders thus constructed into the usual renormalization s theme . It is shown further that infrared divergences can be treated in a very similar way. Our method i...

The authors have implemented three numerical quadrature schemes, using the Arbitrary Precision (ARPREC) software package. The objective here is a quadrature facility that can efficiently evaluate to very high precision a large class of integrals typical of those encountered in experimental mathematics, relying on a minimum of a priori information regarding the function to be integrated. Such a ...

We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.