Order adaptive integration rule with equivalently weighted internal nodes

Minvydas Ragulskis (Department of Mathematical Research in Systems, Kaunas University of Technology, Kaunas, Lithuania)
Liutauras Ragulskis (Department of Informatics, Vytautas Magnus University, Kaunas, Lithuania)

Engineering Computations

ISSN: 0264-4401

Publication date: 1 June 2006



To develop order adaptive integration rule without limitation requiring that the number of equally spaced nodes must be a divisible numeral. Such integration technique could be of great practical value for different engineering applications where partition adaptability is impossible and use of standard high order integration techniques is unfeasible due to the fact that a significant number of nodes at the end of the sampling sequence must be deleted until the needed divisibility of the number of nodes is achieved.


Finite element approximation is used for the subdivision of the domain of integration and the development of order adaptive integration rule.


New integration rule is developed. It has a number of interesting features. Weights of the internal nodes are equivalent and equal to one. That makes the computational implementation of the integration rule very easy. Weights not equal to one are located only at the beginning and at the end of the sequence and are symmetric. For an m‐th order rule the number of weights not equal to one is 2m if m is odd.


For different engineering applications where the integration order can be controlled without changing the number of nodes, especially for real time applications where the number of discrete samples is unknown before the experiment.



Ragulskis, M. and Ragulskis, L. (2006), "Order adaptive integration rule with equivalently weighted internal nodes", Engineering Computations, Vol. 23 No. 4, pp. 368-381. https://doi.org/10.1108/02644400610661154

Download as .RIS



Emerald Group Publishing Limited

Copyright © 2006, Emerald Group Publishing Limited

Please note you might not have access to this content

You may be able to access this content by login via Shibboleth, Open Athens or with your Emerald account.
If you would like to contact us about accessing this content, click the button and fill out the form.
To rent this content from Deepdyve, please click the button.