Implicit–explicit methods based on strong stability preserving multistep time discretizations

摘要

In this note we propose and analyze novel implicit-explicit methods based onsecond order strong stability preserving multistep time discretizations.Several schemes are developed, and a linear stability analysis is performed tostudy their properties with respect to the implicit and explicit eigenvalues.One of the proposed schemesis found to have very good stability properties,with implicit A-stability for the entire explicit stability domain. Theproperties of the other proposed schemes are comparable to those of traditionalmethods found in the literature.