On Two Families of Implicit Interval Methods of Adams-Moulton Type

• Autorzy: Jankowska, M. , Marciniak, A.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

initial-value problem; interval methods; floating point interval arithmetic

• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2006
• Tom: Vol. 12, nr 2
• Strony: 109-113
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Jankowska, M.

autor

Marciniak, A.

• Poznań University of Technology, Institute of Applied Mechanics Piotrowo 3, 60-965 Poznań, Poland,

Bibliografia

• [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 IntervalMultistep 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 ValueProblems 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.