Title: Lie group integrators with non-autonomous frozen vector fields

Authors: Borislav V. Minchev

Addresses: Department of Mathematics, School of Informatics, University of Wales Bangor, Gwynedd, LL57 1UT, UK

Abstract: Lie group methods for non-autonomous semi-discretised in space, partial differential equations are considered. The use of time-dependent frozen vector fields and their corresponding algebra actions on a manifold is introduced. A new integration scheme, for the numerical solution of semi-linear problems, based on the so-called |comutator-free Lie group methods|, with algebra action arising from the proposed new framework is derived. The scheme is then compared with some existing methods in several numerical experiments.

Keywords: algebra action; exponential integrators; Lie group methods; stiff systems; partial differential equations; PDE; time-dependent vector fields; frozen vector fields; Lie group integrators.

DOI: 10.1504/IJCSE.2007.018268

International Journal of Computational Science and Engineering, 2007 Vol.3 No.4, pp.287 - 294

Published online: 14 May 2008 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article