Interval versions of central-difference method for solving the poisson equation in proper and directed interval arithmetic

• Autorzy: Hoffmann T. , Marciniak A. , Szyszka B.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2013
• Tom: Vol. 38, No. 3
• Strony: 193--206
• Opis fizyczny: Bibliogr. 14 poz., tab., fig.

Twórcy

autor

Hoffmann T.

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

autor

Marciniak A.

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

autor

Szyszka B.

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

Bibliografia

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