<abstract xmlns="http://www.w3.org/1999/xhtml"> To study the Poisson equation, the central-difference method is often used. This method has the local truncation error of order O(h2 +k2), where h and k are mesh constants. Using this method in conventional floating-point arithmetic, we get solutions including the method, representation and rounding errors. Therefore, we propose interval versions of the central-difference method in proper and directed interval arithmetic. Applying such methods in floating-point interval arithmetic allows one to obtain solutions including all possible numerical errors. We present numerical examples from which it follows that the presented interval method in directed interval arithmetic is a little bit better than the one in proper interval arithmetic, i.e. the intervals of solutions are smaller. It appears that applying both proper and directed interval arithmetic the exact solutions belong to the interval solutions obtained.</abstract>

To study the Poisson equation, the central-difference method is often used. This method has the local truncation error of order O(h2 +k2), where h and k are mesh constants. Using this method in conventional floating-point arithmetic, we get solutions including the method, representation and rounding errors. Therefore, we propose interval versions of the central-difference method in proper and directed interval arithmetic. Applying such methods in floating-point interval arithmetic allows one to obtain solutions including all possible numerical errors. We present numerical examples from which it follows that the presented interval method in directed interval arithmetic is a little bit better than the one in proper interval arithmetic, i.e. the intervals of solutions are smaller. It appears that applying both proper and directed interval arithmetic the exact solutions belong to the interval solutions obtained.

Interval Versions of Central-Difference Method for Solving the Poisson Equation in Proper and Directed Interval Arithmetic

Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland, Institute of Computing Science

Poznan University of Technology, Piotrowo 3A, 60-965 Poznan, Poland, Institute of Mathematics

Foundations of Computing and Decision Sciences

To study the Poisson equation, the central-difference method is often used. This method has the local truncation error of order O(h2 +k2), where h and k are...

Interval Versions of Central-Difference Method for Solving the Poisson Equation in Proper and Directed Interval Arithmetic

Published Online: Sep 27, 2013

Page range: 193 - 206

DOI: https://doi.org/10.2478/fcds-2013-0009

Keywords
Poisson equation, central-difference method, interval methods, proper interval arithmetic, directed interval arithmetic, floating-point interval arithmetic

This content is open access.

Interval Versions of Central-Difference Method for Solving the Poisson Equation in Proper and Directed Interval Arithmetic

Published Online: Sep 27, 2013

Page range: 193 - 206

DOI: https://doi.org/10.2478/fcds-2013-0009

KeywordsPoisson equation, central-difference method, interval methods, proper interval arithmetic, directed interval arithmetic, floating-point interval arithmetic

This content is open access.

Keywords
Poisson equation, central-difference method, interval methods, proper interval arithmetic, directed interval arithmetic, floating-point interval arithmetic