On Two Families of Implicit Interval Methods of Adams-Moulton Type
Jankowska Małgorzata 1, Marciniak A. 2,3
1 Poznań University of Technology, Institute of Applied Mechanics
Piotrowo 3, 60-965 Poznań, Poland
2 Poznań University of Technology, Institute of Computing Science
Piotrowo 3a, 60-965 Poznań, Poland
3 Adam Mickiewicz University, Faculty of Mathematics and Computer Science
Umultowska 87, 61-614 Poznań, Poland
e-mail: {mjank/anmar}@sol.put.poznan.pl
Received:
Rec. 7 September 2005
DOI: 10.12921/cmst.2006.12.02.109-113
OAI: oai:lib.psnc.pl:618
Abstract:
In our previous paper [1] we have presented implicit interval methods of Adams-Moulton type. It appears that two families of these types of methods exist. We compare both families of methods and present a numerical example.
Key words:
floating-point interval arithmetic, initial value problem, interval methods
References:
[1] M. Jankowska and A. Marciniak, Implicit Interval Multistep Methods for Solving the Initial Value Problem, CMST 8(1), 17-30 (2002).
[2] M. Jankowska and A. Marciniak, On Explicit Interval Methods of Adams-Bashforth Type, CMST 8(2), 46-57 (2002).
[3] M. Jankowska and A. Marciniak, Preliminaries of the IMM System for Solving the Initial Value Problem by Interval Multistep Methods [in Polish], Pro Dialog 10, 117-134 (2005).
[4] L. Jaulin, M. Kieffer, O. Didrit and É. Walter, Applied Interval Analysis, Springer-Verlag, London 2001.
[5] S. A. Kalmykov, Ju. I. Šokin and E. Ch. Juldašev, Methods of Interval Analysis [in Russian], Nauka, Novosibirsk 1986.
[6] A. Krupowicz, Numerical Methods of Initial Value Problems of Ordinary Differential Equations [in Polish], PWN, Warsaw 1986.
[7] A. Marciniak, Implicit Interval Methods for Solving the Initial Value Problem, Numerical Algorithms 37, 241-251 (2004).
[8] A. Marciniak, On Multistep Interval Methods for Solving the Initial Value Problem, Journal of Computational and Applied Mathematics (in press).
[9] R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs 1966.
[10] Ju. I. Šokin, Interval Analysis [in Russian], Nauka, Novosibirsk 1981.
In our previous paper [1] we have presented implicit interval methods of Adams-Moulton type. It appears that two families of these types of methods exist. We compare both families of methods and present a numerical example.
Key words:
floating-point interval arithmetic, initial value problem, interval methods
References:
[1] M. Jankowska and A. Marciniak, Implicit Interval Multistep Methods for Solving the Initial Value Problem, CMST 8(1), 17-30 (2002).
[2] M. Jankowska and A. Marciniak, On Explicit Interval Methods of Adams-Bashforth Type, CMST 8(2), 46-57 (2002).
[3] M. Jankowska and A. Marciniak, Preliminaries of the IMM System for Solving the Initial Value Problem by Interval Multistep Methods [in Polish], Pro Dialog 10, 117-134 (2005).
[4] L. Jaulin, M. Kieffer, O. Didrit and É. Walter, Applied Interval Analysis, Springer-Verlag, London 2001.
[5] S. A. Kalmykov, Ju. I. Šokin and E. Ch. Juldašev, Methods of Interval Analysis [in Russian], Nauka, Novosibirsk 1986.
[6] A. Krupowicz, Numerical Methods of Initial Value Problems of Ordinary Differential Equations [in Polish], PWN, Warsaw 1986.
[7] A. Marciniak, Implicit Interval Methods for Solving the Initial Value Problem, Numerical Algorithms 37, 241-251 (2004).
[8] A. Marciniak, On Multistep Interval Methods for Solving the Initial Value Problem, Journal of Computational and Applied Mathematics (in press).
[9] R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs 1966.
[10] Ju. I. Šokin, Interval Analysis [in Russian], Nauka, Novosibirsk 1981.
