A survey of interval Runge-Kutta and multistep methods for solving the initial value problem

Authors:
Karol Gajda;Małgorzata Jankowska;Andrzej Marciniak;Barbara Szyszka
Affiliations:
Poznan University of Technology, Institute of Mathematics, Poznań, Poland;Poznan University of Technology, Institute of Applied Mechanics, Poznań, Poland;Poznan University of Technology, Institute of Computing Science, Poznań, Poland and Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Poznań, Poland;Poznan University of Technology, Institute of Mathematics, Poznań, Poland
Venue:
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Year:
2007

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Abstract

The paper is dealt with a number of one- and multistep interval methods developed by our team during the last decade. We present implicit interval methods of Runge-Kutta type, interval versions of symplectic Runge-Kutta methods and interval multistep methods of Adams-Bashforth, Adams-Moulton, Nystrm and Milne-Simpson types.