scholarly journals On the relative merits of three-point integration rules for six-node triangles

1997 ◽  
Vol 27 (4) ◽  
pp. 335-343 ◽  
Author(s):  
K.Y. Sze ◽  
D. Zhu
Keyword(s):  
Point Integration ◽  
Integration Rules

Finite-order Integration Weights Can be Dangerous

2007 ◽  
Vol 7 (3) ◽  
pp. 239-254 ◽  
Author(s):  
I.H. Sloan
Keyword(s):  
Function Space ◽  
Finite Order ◽  
Small Subset ◽  
Worst Case ◽  
Integration Rule ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Sum Of Functions ◽  
Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

Properties of Minimal Integration Rules. II

1971 ◽  
Vol 8 (3) ◽  
pp. 497-508 ◽  
Author(s):  
Nira Richter-Dyn
Keyword(s):  
Integration Rules

scholarly journals Revisited Optimal Error Bounds for Interpolatory Integration Rules

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
François Dubeau
Keyword(s):  
Error Bounds ◽  
Error Term ◽  
Quadrature Rules ◽  
Optimal Error ◽  
Integration By Parts ◽  
Integration Rules

We present a unified way to obtain optimal error bounds for general interpolatory integration rules. The method is based on the Peano form of the error term when we use Taylor’s expansion. These bounds depend on the regularity of the integrand. The method of integration by parts “backwards” to obtain bounds is also discussed. The analysis includes quadrature rules with nodes outside the interval of integration. Best error bounds for composite integration rules are also obtained. Some consequences of symmetry are discussed.

Towards Public Services and Process Integration

2013 ◽  
pp. 275-287
Author(s):  
Guillermo Infante Hernández ◽  
Aquilino A. Juan Fuente ◽  
Benjamín López Pérez ◽  
Edward Rolando Núñez-Valdéz
Keyword(s):  
Process Model ◽  
Public Services ◽  
Process Integration ◽  
Domain Specific ◽  
Modeling Environment ◽  
Proposed Model ◽  
Domain Specific Modeling ◽  
Hardware Platforms ◽  
Business Requirements ◽  
Integration Rules

Software platforms for e-government transactions may differ in developed functionalities, languages and technologies, hardware platforms, and operating systems that support them. Those differences can be found among public organizations that share common processes, services, and regulations. This scenario hinders interoperability between these organizations. Hence, to find a technique for integrating these platforms becomes a necessity. In this chapter, a rule-based domain-specific modeling environment for public services and process integration is suggested, which consists of common identified public service elements and a set of process integration rules. This approach provides the needed integration or interoperability pursued in this domain. Furthermore a service and process model is proposed to formalize the information needed for integration of both. A set of integration rules is also presented as part of the modeling environment. This set of integration rules completes the proposed model to meet the business requirements of this domain.

scholarly journals Improving the two-stage numerical integration in stability identification of oscillation with distributed delay

2019 ◽  
Vol 11 (1) ◽  
pp. 168781401881990
Author(s):  
Chigbogu Godwin Ozoegwu
Keyword(s):  
Numerical Integration ◽  
Distributed Delay ◽  
Original Method ◽  
Higher Order ◽  
Trapezoidal Rule ◽  
Point Of View ◽  
Engineering Systems ◽  
Two Stage ◽  
Integration Rule ◽  
Integration Rules

The vibration of the engineering systems with distributed delay is governed by delay integro-differential equations. Two-stage numerical integration approach was recently proposed for stability identification of such oscillators. This work improves the approach by handling the distributed delay—that is, the first-stage numerical integration—with tensor-based higher order numerical integration rules. The second-stage numerical integration of the arising methods remains the trapezoidal rule as in the original method. It is shown that local discretization error is of order [Formula: see text] irrespective of the order of the numerical integration rule used to handle the distributed delay. But [Formula: see text] is less weighted when higher order numerical integration rules are used to handle the distributed delay, suggesting higher accuracy. Results from theoretical error analyses, various numerical rate of convergence analyses, and stability computations were combined to conclude that—from application point of view—it is not necessary to increase the first-stage numerical integration rule beyond the first order (trapezoidal rule) though the best results are expected at the second order (Simpson’s 1/3 rule).

Dissolving Organisational and Technological Silos

2007 ◽  
pp. 1-22 ◽  
Author(s):  
W. Lam ◽  
V. Venky Shankararaman
Keyword(s):  
Business Processes ◽  
Ad Hoc ◽  
Process Integration ◽  
Customer Relationship ◽  
Clear Understanding ◽  
Management Support ◽  
Enterprise Integration ◽  
It Integration ◽  
Point Integration ◽  
Point To Point

Over the last few years, the importance of enterprise integration has grown significantly. As organizations expand, become more distributed, and rely more on technology, there is a need to ensure both business processes and technology systems are co-coordinated in a strategic rather than ad-hoc manner. In the early days of IT, integration was viewed largely as a technical activity. Today, there is a much stronger business focus. In fact, many of an organisation’s strategic initiatives such as e-business, customer relationship management and supply chain management depend upon enterprise integration. There are four basic integration architectures, namely, batch integration, point-to-point integration, broker-based integration and business process integration. Each integration architecture represents varying levels of enterprise integration maturity. Enterprise integration is a significant undertaking, and carries with it significant technical and managerial challenges. Managing enterprise integration projects requires, among other things, a strategic framework, senior management support and risk management. A clear understanding of enterprise integration requirements is also crucial.

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