Friday 29th of March 2024
 

New Generalized Interval Arithmetic and its applications to structural mechanics and electrical circuits


Hassan Badry Mohamed Ahmed El-Owny

In the paper we solve parametric linear systems of equations whose coefficients are , in the general case, nonlinear functions of interval parameters. Here solution means that we enclose the set of all solutions, the so-called parametric solution set, obtained when all parameters are allowed to vary within their intervals. This task appears in many scientific and engineering problems involving uncertainties. A C-XSC implementation of a parametric fixed-point iteration method for computing an outer enclosure for the solution set is proposed in this paper .This method requires to bound the range of a multivariate function over a given box and often delivers intervals which are too wide for practical applications. We computed tight enclosures of the parametric solution set by using a new generalized interval arithmetic which is an arithmetic for intervals (which are representing uncertainties). The most important property of this method is to reduce the effect of the dependency problem which is inherent in the computation with standard interval arithmetic. We used the new arithmetic to tightly bound the range of a multivariate nonlinear function over a box, a task to which many problems in mathematics and its applications can be reduced. We applied the new bounding technique to improve the efficiency of the solution for parametric systems. Numerical examples illustrating the applicability of the proposed method are solved, and compared with other methods.

Keywords: Interval Arithmetic, dependency problem, validated interval software, parametric interval systems, C-XSC, electrical circuits, structural mechanics.

Download Full-Text


ABOUT THE AUTHOR

Hassan Badry Mohamed Ahmed El-Owny
Hassan Badry Mohamed A. El-Owny is Assistant Professor of Computer Science at Faculty of Science, Aswan University, Aswan, Egypt. His current position is Assistant Proffersor at Taif University, Taif, KSA. He received the PhD degree in ``Computer Science'' at University of Wuppertal(Germany). He is an Aboard Editor of several international journals. He has published extensively in internationally refereed journals and conferences. His main research interests are: Scientific Computing, Computer Algebra, Interval Arithmatics, Parametric systems, Approximation of Uncertain Data and Software Tools with Result Verification.


IJCSI Published Papers Indexed By:

 

 

 

 
+++
About IJCSI

IJCSI is a refereed open access international journal for scientific papers dealing in all areas of computer science research...

Learn more »
Join Us
FAQs

Read the most frequently asked questions about IJCSI.

Frequently Asked Questions (FAQs) »
Get in touch

Phone: +230 911 5482
Email: info@ijcsi.org

More contact details »