Solving the Poisson Equation by an Interval Difference Method of the Second Order

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

Abstrakty

EN

The paper deals with an interval difference method for solving the Poisson equation based on the conventional central-difference method. We present the interval method in full details. The method is constructed in such a way that the exact solution is included in the interval solution obtained. Some numerical results obtained in floating-point interval arithmetic are also presented

Słowa kluczowe

EN

Poisson's equation; central-difference method; interval difference method

• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2013
• Tom: Vol. 19, No. 1
• Strony: 13--21
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Hoffmann, T.

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

autor

Marciniak, A.

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

Bibliografia

• [1] R.L. Burden, J. D. Faires, Numerical Analysis, 3rd Edition, Prindle, Weber & Schmidt, Boston 1981.
• [2] R. Hammer, M. Hocks, U. Kulisch, D. Ratz, Numerical Toolbox for Verified Computing I: Basic Numerical Problems, Springer, Berlin 1993.
• [3] D. Kincaid, W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Edition, Broks/ Cole, Pacific Grove 2002.
• [4] A. Marciniak, Implicit Interval Methods for Solving the Initial Value Problem, Numerical Algorithms 37, 241-251 (2004).
• [5] A. Marciniak, Multistep Interval Methods of Nyström and Milne-Simpson Types, Computational Methods in Science and Technology 13(1), 23-40 (2007).
• [6] A. Marciniak, On Multistep Interval Methods for Solving the Initial Value Problem, Journal of Computational and Applied Mathematics 199(2), 229-238 (2007).
• [7] A. Marciniak, Selected Interval Methods for Solving the Initial Value Problem, Publishing House of Pozna´n University of Technology, Pozna´n 2009.
• [8] R.E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs 1966.
• [9] J.I. Shokin, Interval Analysis [in Russian], Nauka, Novosibirsk 1982.