Solving the Poisson Equation by an Interval Difference Method of the Second Order
Poznań University of Technology, Institute of Computing Science, Piotrowo 2, 60-965 Poznań, Poland
E-mail: tomaszhof@gmail.com, Andrzej.Marciniak@put.poznan.pl
Received:
(Received: 15 January 2012; revised: 7 January 2013; accepted: 7 January 2013; published online: 22 January 2013)
DOI: 10.12921/cmst.2013.19.01.13-21
OAI: oai:lib.psnc.pl:428
Abstract:
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.
Key words:
central-difference method, interval difference method, Poisson’s equation
References:
[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 (2004), 241–251.
[5] A. Marciniak, Multistep Interval Methods of Nyström and Milne-Simpson Types, Computational Methods in Science and Technology 13 (1) (2007), 23–40.
[6] A. Marciniak, On Multistep Interval Methods for Solving the Initial Value Problem, Journal of Computational and Applied Mathematics 199 (2) (2007), 229–238.
[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
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.
Key words:
central-difference method, interval difference method, Poisson’s equation
References:
[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 (2004), 241–251.
[5] A. Marciniak, Multistep Interval Methods of Nyström and Milne-Simpson Types, Computational Methods in Science and Technology 13 (1) (2007), 23–40.
[6] A. Marciniak, On Multistep Interval Methods for Solving the Initial Value Problem, Journal of Computational and Applied Mathematics 199 (2) (2007), 229–238.
[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
