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

In this note we propose and analyze novel implicit-explicit methods based on second order strong stability preserving multistep time discretizations. Several schemes are developed, and a linear stability analysis is performed to study 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. The properties of the other proposed schemes are comparable to those of traditional methods found in the literature.