Tranquilli, PaulSandu, AdrianZhang, H.2017-03-062017-03-062016-11-22http://hdl.handle.net/10919/75258This paper develops a new class of linearly implicit time integration schemes called Linearly-Implicit Runge-Kutta-W (LIRK-W) methods. These schemes are based on an implicit-explicit approach which does not require a splitting of the right hand side and allow for arbitrary, time dependent, and stage varying approximations of the linear systems appearing in the method. Several formulations of LIRK-W schemes, each designed for specific approximation types, and their associated order condition theories are presented.enIn Copyrightmath.NAArticle - Refereed