W. Auzinger, M. Lapinska:
"Convergence of rational multistep methods of Adams-Padé type";
BIT Numerical Mathematics, 52 (2012), ISBN: 978-3-902627-04-9; S. 3 - 20.

Kurzfassung englisch:
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, Pad´e approximation, convergence

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Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.