BIT Numerical Mathematics

, Volume 52, Issue 1, pp 3–20 | Cite as

Convergence of rational multistep methods of Adams-Padé type

  • Winfried AuzingerEmail author
  • Magdalena Łapińska


Rational generalizations of multistep schemes, where the linear stiff part of a given problem is treated by an A-stable rational approximation, have been proposed by several authors, but a reasonable convergence analysis for stiff problems has not been provided so far. In this paper we directly relate this approach to exponential multistep methods, a subclass of the increasingly popular class of exponential integrators. This natural, but new interpretation of rational multistep methods enables us to prove a convergence result of the same quality as for the exponential version. In particular, we consider schemes of rational Adams type based on A-acceptable Padé approximations to the matrix exponential. A numerical example is also provided.


Rational multistep schemes Stiff initial value problems Evolution equations Adams schemes Padé approximation Convergence 

Mathematics Subject Classification (2000)

65L06 65L20 65M12 


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© Springer Science + Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria
  2. 2.Department of Mathematical and Numerical AnalysisGdańsk University of TechnologyGdańskPoland

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