Publications in Scientific Journals:
W. Auzinger, M. Lapinska:
"Convergence of rational multistep methods of Adams-Padé type";
BIT Numerical Mathematics,
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, PadŽe approximation, convergence
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.