Talks and Poster Presentations (with Proceedings-Entry):
W. Auzinger, M. Lapinska:
"Rational multistep methods via modified phi_j - functions";
Talk: GAMM Jahrestagung 2011,
Graz (invited);
04-18-2011
- 04-21-2011; in: "Proceedings of the GAMM 82nd Annual Scientific Conference, Graz, Austria, April 18-21, 2011",
PAMM,
11
(2011),
ISSN: 1617-7061;
757 pages.
English abstract:
We consider semilinear stiff evolution equations of the type u'=Au+g(t,u). Exponential methods of Adams-type have recently been analyzed by several authors. In many applications, the matrix exponential exp(hA) and the corresponding 'phi-functions' are approximated using Krylov subspace techniques and, e.g., using Padé approximations in a projected space.
Replacing exp(hA) by an A-acceptable Padé approximation R(hA) in the recursion for the coefficient matrices gives rise to rational Adams-type schemes comprising methods proposed earlier. For this 'Adams-Padé'method, convergence analogous to the exponential version can be proved. For a Krylov implementation this suggests to use Padé approximants of appropriate fixed order; this is subject to further investigation.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1002/pamm.201110368
Created from the Publication Database of the Vienna University of Technology.