Contributions to Books:
W. Auzinger, M. Lapinska:
"Convergence of rational multistep methods of Adams-Padé type";
in: "ASC Report 05/2011",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
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
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.